%{search_type} search results

• The main construction and outline of the proof
• Preliminary estimates
• The nonlinearities N^h/[infinity][beta] and n^[psi]
• Improved energy estimates
• Improved profile bounds
• The main theorems

"This monograph presents a significant new result in general relativity. In particular, it provides a proof related to the Einstein-Klein-Gordon equation, a fundamental equation in mathematical physics that couples the Einstein equation of general relativity with a matter field described by the Klein-Gordon equation. The book begins with an introduction and history of the subject, proceeds to prove several auxiliary lemmas, and culminates in the central proof. This book represents a significant advance in mathematical physics, and provides the most cutting-edge treatment of the Einstein-Klein-Gordon equation to date"-- Provided by publisher

• Maxwellʼs Equations
• Electromagnetic Waves
• Jump and Boundary Conditions
• Two Fundamental Polarizations
• References
• Diffraction Grating Theory
• Perfectly Conducting Gratings
• Dielectric Gratings
• Biperiodic Gratings
• Perfect Electric Conductors
• Dielectric Media
• References
• Variational Formulations
• The Dirichlet Problem
• The Transmission Problem
• Biperiodic Structures
• Function Spaces
• The Transparent Boundary Condition
• The Variational Problem
• References
• Finite Element Methods
• The Finite Element Method
• Finite Element Analysis for TE Polarization
• Finite Element Analysis for TM Polarization
• Adaptive Finite Element PML Method
• The PML Formulation
• Transparent Boundary Condition for the PML Problem
• Error Estimate of the PML Solution
• The Discrete Problem
• Error Representation Formula
• A Posteriori Error Analysis
• Numerical Results
• Adaptive Finite Element DtN Method
• The Discrete Problem
• A Posteriori Error Analysis
• TM Polarization
• Numerical Results
• Adaptive Finite Element PML Method for Biperiodic Structures
• The PML Formulation
• Transparent Boundary Condition for the PML Problem
• Convergence of the PML Solution
• The Discrete Problem
• A Posteriori Error Analysis
• Numerical Results
• References
• Inverse Diffraction Grating
• Uniqueness Theorems
• The Helmholtz Equation
• Maxwellʼs Equations
• Local Stability
• The Helmholtz Equation
• Maxwellʼs Equations
• Numerical Methods
• References
• Near-Field Imaging
• Near-Field Data
• The Variational Problem
• An Analytic Solution
• Convergence of the Power Series
• The Reconstruction Formula
• Error Estimates
• Numerical Results
• Far-Field Data
• The Reduced Problem
• Transformed Field Expansion
• The Reconstruction Formula
• A Nonlinear Correction Scheme
• Numerical Results
• Maxwellʼs Equations
• The Reduced Model Problem
• Transformed Field Expansion
• The Zerolh Order Term
• The First Order Term
• The Reconstruction Formula
• Numerical Results
• References
• Related Topics
• Method of Boundary Integral Equations
• Model Problems
• Quasi-periodic Greenʼs Function
• Boundary Integral Operators
• Boundary Integral Equations
• Integral Formulas for Rayleighʼs Coefficients
• Time-Domain Problems
• Problem Formulation
• Time-Domain Transparent Boundary Condition
• The Reduced Problem
• A Priori Estimates
• Nonlinear Gratings
• SHG Model
• TE-TE Polarization
• TM-TE Polarization
• Optimal Design Problems
• The Model Problem
• The Optimal Design Problem
• Homogenization of the Design Problem
• The Relaxed Problem
• References
• Appendices
• Index

This book addresses recent developments in mathematical analysis and computational methods for solving direct and inverse problems for Maxwell's equations in periodic structures. The fundamental importance of the fields is clear, since they are related to technology with significant applications in optics and electromagnetics. The book provides both introductory materials and in-depth discussion to the areas in diffractive optics that offer rich and challenging mathematical problems. It is also intended to convey up-to-date results to students and researchers in applied and computational mathematics, and engineering disciplines as well.
(source: Nielsen Book Data)

This book honors the remarkable science and life of Shoucheng Zhang, a condensed matter theorist known for his work on topological insulators, the quantum Hall effect, spintronics, superconductivity, and other fields. It contains the contributions displayed at the Shoucheng Zhang Memorial Workshop held on May 2-4, 2019 at Stanford University.
(source: Nielsen Book Data)

• Recovery: the second disaster
• Mitigation: preventing disaster
• Response: the disaster
• Damage control
• Preparedness: anticipating disaster
• Disaster justice

"In Disasterology, Dr. Montano, a disaster researcher, brings readers with her on an eye-opening journey through some of our worst disasters, helping readers make sense of what really happened from a emergency management perspective. She explains why we aren't doing enough to prevent or prepare for disasters, the critical role of media, and how our approach to recovery was not designed to serve marginalized communities. Now that climate change is contributing to the disruption of ecosystems and worsening disasters, Dr. Montano offers a preview of what will happen to our communities if we don't take aggressive, immediate action. In a section devoted to the COVID-19 pandemic, what is thus far our generation's most deadly disaster, she casts light on the many decisions made behind closed doors that failed to protect the public"-- Provided by publisher

• UNIT I: SETTING THE STAGE
• Chapter 1. Approaches in Global Change Biology How Did the Field of Global Change Biology Develop? How Are Global Change Biology Studies Designed? What Key Research Approaches Are Used in Global Change Biology? What Key Tools Are Used in Global Change Biology? Core Concepts: How are Data Displayed? Meet the Data: The Economic Value of Nature Taking a Closer Look: The Value of Biological Diversity
• Chapter 2. Brief History of Life on Earth What Key Transitions Led to the Emergence of Life on Earth? How Did Cellular Life Evolve and Diversify? What Evolutionary Processes Shape Biological Diversity? When Have Speciation and Extinction Rates Been Particularly High? Core Concepts: What is a Phylogenetic Tree? Meet the Data: The Ring of Life Taking a Closer Look: Biological Levels of Change
• Chapter 3. Rise of the Humans When and How Did Early Hominids Evolve? When and How Did Modern Humans Spread Around the World? How Did Early Human Civilizations Impact the Environment? Core Concepts: What Is In a Name? Meet the Data: Ice Age Genetics Taking a Closer Look: The Evolutionary Success of Humans
• Chapter 4. The Anthropocene What Is the Anthropocene and When Did It Begin? What Are Patterns of Contemporary Population Growth? How Are Contemporary Human Civilizations Impacting the Environment? How Do Anthropogenic Stressors Interact with Each Other? What Influences Overall Vulnerability to Global Change Pressures? Core Concepts: What is Climate and How Is It Measured? Meet the Data: Pollinators and Pesticides Taking a Closer Look: Historical and Contemporary Climate Change UNIT II: CORE RESPONSES TO GLOBAL CHANGE STRESSORS
• Chapter 5. Core Responses: Move How and Why Do Organisms Move? What Is a Geographic Range? What Factors Determine a Species' Geographic Range? Do Range Changes Occur Even Without Anthropogenic Influence? What Types of Range Changes Occur in Response to Anthropogenic Pressures? How Do Scientists Predict Range Changes? Core Concepts: What Is a Niche? Meet the Data: A Century of Change in Yosemite Taking a Closer Look: Globalization and Invasive Species
• Chapter 6. Core Responses: Adjust What Is Phenotypic Plasticity? Is the Capacity for Plasticity Consistent Across Traits and Species? What Types of Plasticity Occur in Response to Global Change What Mechanisms Underlie Phenotypic Plasticity? How Do Scientists Assess and Predict Phenotypic Plasticity? Can Plasticity Facilitate Long-Term Persistence? Core Concepts: What Are the Mechanisms of Heredity? Meet the Data: Phenology and Global Warming Taking a Closer Look: Urbanization
• Chapter 7. Core Responses: Adapt What Conditions Are Required for Adaptation? What Is an Example of Evolution by Natural Selection? What Types of Adaptation Occur in Response to Global Change Pressures? How Do Scientists Identify Adaptations and Predict Adaptive Potential? Can Adaptation Prevent Extinction? Core Concepts: Where Does Genetic Variation Come From? Meet the Data: The Daphnia Time Machine Taking a Closer Look: Coral Reefs
• Chapter 8. Core Responses: Die How Is the Survival of Individuals, Populations, and Species Connected? What Are Examples of Extinction in Response to Global Change Pressures? How Do Scientists Estimate Extinction Risk? How Do Scientists Summarize Global Patterns of Extinction Risk? What Is the Sixth Mass Extinction? Core Concepts: What is Extinction Debt? Meet the Data: The Sixth Mass Extinction Taking a Closer Look: Amphibian Declines UNIT III: COMPLEX RESPONSES TO GLOBAL CHANGE PRESSURES
• Chapter 9. Community-Level Responses What Are Key Types of Biological Interactions? How Do Global Change Pressures Affect Biological Interactions? How Does Extinction Affect Communities? What Are Cascading Effects? Core Concepts: What Are Above- and Below-Ground Food Webs? Meet the Data: The Collapse of Mutualisms Taking a Closer Look: Kelp Forests and Trophic Cascades
• Chapter 10. Ecosystem-Level Responses What Are Biogeochemical Cycles? How Do Global Change Pressures Impact Ecosystems? How Do Global Change Pressures Impact Large-Scale Earth Systems? What Is a Feedback? What Is Ecosystem Collapse? What Is Ecosystem Resilience? Core Concepts: What is a Biodiversity Hotspot? Meet the Data: Greenhouse Gases in the Soil Taking a Closer Look: Factors Influencing Response to Global Change UNIT IV: NEW HORIZONS
• Chapter 11. Conservation in an Era of Global Change Why Is It Important to Explicitly Define Conservation Priorities? Why Is It Important to Match Conservation Actions to Particular Biological Levels? What Are Examples of Fine-Filter Conservation Strategies? What Are Examples of Coarse-Filter Conservation Strategies? What Is Adaptive Management? Core Concepts: What is Climate Mitigation? Meet the Data: Maximizing Evolutionary Diversity Taking a Closer Look: Emerging Technologies and Conservation Ethics
• Chapter 12. Aligning the Interests of Biodiversity and Human Society What Are Coupled Human-Natural Systems? What Societal Levers Can Be Used to Support Biodiversity Conservation? How Can Individuals Support Biodiversity Conservation? How Can Collectives Support Biodiversity Conservation? How Can Policy Action Support Biodiversity Conservation? What Is the Forecast for the Future? Core Concepts: What is I=PAT? Meet the Data: Financial Incentives for Dynamic Conservation Taking a Closer Look: Environmental Worldviews.
• (source: Nielsen Book Data)

Bree Rosenblum's Global Change Biology provides a comprehensive introduction to the field of Global Change Biology and a roadmap for structuring Global Change Biology courses, a burgeoning field of biological study. The first of its kind, Rosenblum goes beyond the narrow focus of existing texts, which tend to focus on climate only, by offering a conceptionally integrated approach to understanding how humans have impacted life on Earth. The textbook guides students to think about change across spatial and temporal scales and fills a unique niche of integrating ecological and evolutionary perspectives throughout. Global Change Biology is available in e-book format only. Print-on-demand can be provided for orders where print is specified. The conceptual arc of the textbook is organized around four fundamental learning objectives that traverse the past, present, and future. Students will explore: a) the complex history of planetary change, b) the impact of contemporary stressors across biological levels, biomes, and the tree of life, c) the dynamic interactions and responses of living systems to planetary change, and d) the opportunities for maintaining resilient ecosystems in a changing world. Enrichment features include Core Concepts boxes reviewing foundational material, Meet the Data boxes providing direct experience interpreting global change biology data, and Taking a Closer Look providing an opportunity to evaluate multifaceted biological responses in complex systems. Pre- and post- assessment tools like The Blank Page and reflection questions throughout, encourage students to reflect, self-assess, and deepen their learning. The primary intended audience for Global Change Biology is upper division undergraduate students who are ready to apply key concepts in ecology and evolution to the Global Change Biology theme area and develop a more analytical and integrative skill set as scientists. However, the textbook has crossover power to engage other audiences and provide a roadmap for developing courses to inform and inspire students about the study of life on a rapidly changing planet.
(source: Nielsen Book Data)

• Preface
• Mechanics of Random Motion
• Smooth Motion and Random Motion
• On Stochastic Processes
• Itô's Path Analysis
• Equation of Motion for a Stochastic Process
• Kinematics of Random Motion
• Free Random Motion of a Particle
• Hooke's Force
• Hooke's Force and an Additional Potential
• Complex Evolution Functions
• Superposition Principle
• Entangled Quantum Bit
• Light Emission from a Silicon Semiconductor
• The Double-Slit Problem
• Double-Slit Experiment with Photons
• Theory of Photons
• Principle of Least Action
• Transformation of Probability Measures
• Schrödinger Equation and Path Equation
• Applications
• Motion induced by the Coulomb Potential
• Charged Particle in a Magnetic Field
• Aharonov-Bohm Effect
• Tunnel Effect
• Bose-Einstein Distribution
• Random Motion and the Light Cone
• Origin of the Universe
• Classification of Boundary Points
• Particle Theory of Electron Holography
• Escherichia coli and Meson models
• High-Temperature Superconductivity
• Momentum, Kinetic Energy, Locality
• Momentum and Kinetic Energy
• Matrix Mechanics
• Function Representations of Operators
• Expectation and Variance
• The Heisenberg Uncertainty Principle
• Kinetic Energy and Variance of Position
• Theory of Hidden Variables
• Einstein's Locality
• Bell's Inequality
• Local Spin Correlation Model
• Long-Lasting Controversy and Random Motion
• Markov Processes
• Time-Homogeneous Markov Proces-ses
• Transformations by M-Functionals
• Change of Time Scale
• Duality and Time Reversal
• Time Reversal, Last Occurrence Time
• Time Reversal, Equations of Motion
• Conditional Expectation
• Paths of Brownian Motion
• Applications of Relative Entropy
• Relative Entropy
• Variational Principle
• Exponential Family of Distributions
• Existence of Entrance and Exit Functions
• Cloud of Paths
• Kac's Phenomenon of Propagation of Chaos
• Extinction and Creation
• Extinction of Particles
• Piecing-Together Markov Processes
• Branching Markov Processes
• Construction of Branching Markov Processes
• Markov Processes with Age
• Branching Markov Processes with Age
• Bibliography
• Index

This book discusses quantum theory as the theory of random (Brownian) motion of small particles (electrons etc.) under external forces. Implying that the Schroedinger equation is a complex-valued evolution equation and the Schroedinger function is a complex-valued evolution function, important applications are given. Readers will learn about new mathematical methods (theory of stochastic processes) in solving problems of quantum phenomena. Readers will also learn how to handle stochastic processes in analyzing physical phenomena.
(source: Nielsen Book Data)

• Introduction to field theory
• Classical field theory
• Classical symmetries and conservation laws
• Canonical quantization
• Path integrals in quantum mechanics and quantum field theory
• Nonrelativistic field theory
• Quantization of the free Dirac field
• Coherent-state path-integral quantization of quantum field theory
• Quantization of gauge fields
• Observables and propagators
• Perturbation theory and Feynman diagrams
• Vertex functions, the effective potential and symmetry breaking
• Perturbation theory, regularization and renormalization
• Quantum field theory and statistical mechanics
• The renormalization group
• The perturbative renormalization group
• The 1/N expansions
• Phases of gauge theory
• Instantons and solitons
• Anomalies in quantum field theory
• Conformal field theory
• Topological field theory

The only graduate-level textbook on quantum field theory that fully integrates perspectives from high-energy, condensed-matter, and statistical physics Quantum field theory was originally developed to describe quantum electrodynamics and other fundamental problems in high-energy physics, but today has become an invaluable conceptual and mathematical framework for addressing problems across physics, including in condensed-matter and statistical physics. With this expansion of applications has come a new and deeper understanding of quantum field theory-yet this perspective is still rarely reflected in teaching and textbooks on the subject. Developed from a year-long graduate course Eduardo Fradkin has taught for years to students of high-energy, condensed-matter, and statistical physics, this comprehensive textbook provides a fully "multicultural" approach to quantum field theory, covering the full breadth of its applications in one volume. Brings together perspectives from high-energy, condensed-matter, and statistical physics in both the main text and exercises Takes students from basic techniques to the frontiers of physics Pays special attention to the relation between measurements and propagators and the computation of cross sections and response functions Focuses on renormalization and the renormalization group, with an emphasis on fixed points, scale invariance, and their role in quantum field theory and phase transitions Other topics include non-perturbative phenomena, anomalies, and conformal invariance Features numerous examples and extensive problem sets Also serves as an invaluable resource for researchers.
(source: Nielsen Book Data)

• Introduction to gauge theory / A. Haydys
• Knots, polynomials, and categorification / Jacob Rasmussen
• Lecture notes on Heegard Floer homology / Jennifer Hom
• Advanced topics in gauge theory: mathematics and physics of Higgs bundles / Laura P. Schaposnik
• Gauge theory and a few applications to knot theory / Tomasz S. Mrowka and Donghao Wang
• Lectures on invertible field theories / Soren Galatius
• Topological quantum field theories, knots and BPS states / Pavel Putrov
• Lectures on BPS states and spectral networks / Andrew Neitzke

This volume contains lectures from the Graduate Summer School ""Quantum Field Theory and Manifold Invariants"" held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
(source: Nielsen Book Data)

• Foreword / Yuri I. Manin
• Feynman integrals in mathematics and physics / Spencer Bloch
• Feynman integrals and periods in configuration spaces / Özgür Ceyhan and Matilde Marcolli
• Introductory course on l-adic sheaves and their ramification theory on curves / Lars Kindler and Kay Rülling

This is the first volume of the lectures presented at the Clay Mathematics Institute 2014 Summer School, "Periods and Motives: Feynman amplitudes in the 21st century", which took place at the Instituto de Ciencias Matematicas-ICMAT (Institute of Mathematical Sciences) in Madrid, Spain. It covers the presentations by S. Bloch, by M. Marcolli and by L. Kindler and K. Rulling. The main topics of these lectures are Feynman integrals and ramification theory. On the Feynman integrals side, their relation with Hodge structures and heights as well as their monodromy are explained in Bloch's lectures. Two constructions of Feynman integrals on configuration spaces are presented in Ceyhan and Marcolli's notes. On the ramification theory side an introduction to the theory of l -adic sheaves with emphasis on their ramification theory is given. These notes will equip the reader with the necessary background knowledge to read current literature on these subjects.
(source: Nielsen Book Data)

The essential primer for physics students who want to build their physical intuition Presented in A. Zee's incomparably engaging style, this book introduces physics students to the practice of using physical reasoning and judicious guesses to get at the crux of a problem. An essential primer for advanced undergraduates and beyond, Fly by Night Physics reveals the simple and effective techniques that researchers use to think through a problem to its solution-or failing that, to smartly guess the answer-before starting any calculations. In typical physics classrooms, students seek to master an enormous toolbox of mathematical methods, which are necessary to do the precise calculations used in physics. Consequently, students often develop the unfortunate impression that physics consists of well-defined problems that can be solved with tightly reasoned and logical steps. Idealized textbook exercises and homework problems reinforce this erroneous impression. As a result, even the best students can find themselves completely unprepared for the challenges of doing actual research. In reality, physics is replete with back of the envelope estimates, order of magnitude guesses, and fly by night leaps of logic. Including exciting problems related to cutting-edge topics in physics, from Hawking radiation to gravity waves, this indispensable book will help students more deeply understand the equations they have learned and develop the confidence to start flying by night to arrive at the answers they seek. For instructors, a solutions manual is available upon request.
(source: Nielsen Book Data)

• General introduction Derivation of the weakly nonlinear amplitude equation Existence of exact solutions Approximate solutions Error Analysis and proof of Theorem 3.8 Some extensions Appendix A. Singular pseudodifferential calculus for pulses Bibliography.
• (source: Nielsen Book Data)

This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as ``the amplitude equation'', is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions $u^{\varepsilon} $ to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength $\varepsilon $, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to $u^{\varepsilon}$ on a time interval independent of $\varepsilon $. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.
(source: Nielsen Book Data)

"We prove Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions using Sobolev spaces which impose minimal regularity requirements on pairs of connections and sections. The Lojasiewicz-Simon gradient inequalities for coupled Yang-Mills energy functions generalize that of the pure Yang-Mills energy function due to the first author (Feehan, 2014) for base manifolds of arbitrary dimension and due to R"ade (1992, Proposition 7.2) for dimensions two and three"-- Provided by publisher

• 1. Fundamental concepts
• 2. Quantum dynamics
• 3. Theory of angular momentum
• 4. Symmetry in quantum mechanics
• 5. Approximation methods
• 6. Scattering theory
• 7. Identical particles
• 8. Relativistic quantum mechanics
• Appendix A. Electromagnetic units
• Appendix B. Elementary solutions to Schroedinger's wave equation
• Appendix C. Hamiltonian for a charge in an electromagnetic field
• Appendix D. Proof of the angular-momentum addition rule (3.8.38)
• Appendix E. Finding Clebsch-Gordan coefficients
• Appendix F. Notes on complex variables.
• (source: Nielsen Book Data)

Modern Quantum Mechanics is a classic graduate level textbook, covering the main concepts from quantum mechanics in a clear, organized and engaging manner. The original author, J. J. Sakurai, was a renowned particle theorist. This third edition, revised by Jim Napolitano, introduces topics that extend its value into the twenty-first century, such as modern mathematical techniques for advanced quantum mechanical calculations, while at the same time retaining fundamental topics such as neutron interferometer experiments, Feynman path integrals, correlation measurements, and Bell's inequalities. A solutions manual is available.
(source: Nielsen Book Data)

• volume 1. Basic concepts, tools, and applications
• volume 2. Angular momentum, spin, and approximation methods
• volume 3. Fermions, bosons, photons, correlations, and entanglement

This new edition of the unrivalled textbook introduces the fundamental concepts of quantum mechanics such as waves, particles and probability before explaining the postulates of quantum mechanics in detail. In the proven didactic manner, the textbook then covers the classical scope of introductory quantum mechanics, namely simple two-level systems, the one-dimensional harmonic oscillator, the quantized angular momentum and particles in a central potential. The entire book has been revised to take into account new developments in quantum mechanics curricula. The textbook retains its typical style also in the new edition: it explains the fundamental concepts in chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications. * The quantum mechanics classic in a new edition: written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloe * As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly * Comprehensive: in addition to the fundamentals themselves, the book contains more than 350 worked examples plus exercises Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Superieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the College des France. His main research interests were optical pumping, quantum optics and atom-photon interactions. In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D. Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms. Bernard Diu was Professor at the Denis Diderot University (Paris VII). He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics. Franck Laloe was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Superieure in Paris. His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center. His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.
(source: Nielsen Book Data)
This new, third volume of Cohen-Tannoudji's groundbreaking textbook covers advanced topics of quantum mechanics such as uncorrelated and correlated identical particles, the quantum theory of the electromagnetic field, absorption, emission and scattering of photons by atoms, and quantum entanglement. Written in a didactically unrivalled manner, the textbook explains the fundamental concepts in seven chapters which are elaborated in accompanying complements that provide more detailed discussions, examples and applications. * Completing the success story: the third and final volume of the quantum mechanics textbook written by 1997 Nobel laureate Claude Cohen-Tannoudji and his colleagues Bernard Diu and Franck Laloe * As easily comprehensible as possible: all steps of the physical background and its mathematical representation are spelled out explicitly * Comprehensive: in addition to the fundamentals themselves, the books comes with a wealth of elaborately explained examples and applications Claude Cohen-Tannoudji was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Superieure in Paris where he also studied and received his PhD in 1962. In 1973 he became Professor of atomic and molecular physics at the College des France. His main research interests were optical pumping, quantum optics and atom-photon interactions. In 1997, Claude Cohen-Tannoudji, together with Steven Chu and William D. Phillips, was awarded the Nobel Prize in Physics for his research on laser cooling and trapping of neutral atoms. Bernard Diu was Professor at the Denis Diderot University (Paris VII). He was engaged in research at the Laboratory of Theoretical Physics and High Energy where his focus was on strong interactions physics and statistical mechanics. Franck Laloe was a researcher at the Kastler-Brossel laboratory of the Ecole Normale Superieure in Paris. His first assignment was with the University of Paris VI before he was appointed to the CNRS, the French National Research Center. His research was focused on optical pumping, statistical mechanics of quantum gases, musical acoustics and the foundations of quantum mechanics.
(source: Nielsen Book Data)

Speckle, a granular structure appearing in images and diffraction patterns produced by objects that are rough on the scale of an optical wavelength, is a ubiquitous phenomenon, appearing in optics, acoustics, microwaves, and other fields. This book provides comprehensive coverage of this subject, including both the underlying statistical theory and the applications of this phenomenon. This second edition offers improvements of several topics and addition of significant amounts of new material, including discussion of: generalized random walks, speckle in the eye, polarization speckle (and the statistics of the Stokes parameters in a speckle pattern), the effects of angle and wavelength changes on speckle, the statistics of speckle from "smooth" surfaces, and a spectrometer based on speckle. Many new references are also included. As with the first edition, a multitude of areas of application are covered.
(source: Nielsen Book Data)

• Preface
• Acknowledgements
• 1. Vectors and functions
• 2. Operators and Eigenfunctions
• 3. The Schroedinger equation
• 4. Solving the Schroedinger equation
• 5. Solutions for specific potentials
• References
• Index.
• (source: Nielsen Book Data)

Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schroedinger equation and to analyze the resulting wave functions. Retaining the popular approach used in Fleisch's other Student's Guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schroedinger equation in quantum mechanics. It addresses in a clear and intuitive way the problems students find most troublesome. Each chapter includes several homework problems with fully worked solutions. A companion website hosts additional resources, including a helpful glossary, Matlab code for creating key simulations, revision quizzes and a series of videos in which the author explains the most important concepts from each section of the book.
(source: Nielsen Book Data)

• Climatic and eco-epidemiological aspects of zoonotic cutaneous leishmaniasis in Ouarzazate Province, Morocco / Ahmed Karmaoui
• Seasonal distribution of zoonotic cutaneous leishmaniasis, in Middle Draa Valley, south of Morocco / Ahmed Karmaoui, Siham Zerouali
• Water-climate-leishmaniasis nexus in an endemic focus of zoonotic cutaneous leishmaniasis, the Middle Draa Valley, Morocco / Ahmed Karmaoui, Siham Zerouali
• Associations between climate and the activity of the phlebotomus papatasi, vector of cutaneous leishmaniasis / Ahmed Karmaoui, Siham Zerouali
• Environmental vulnerability and the need to establish long-term ecological research network in Morocco (Mo-LTER) / Ahmed Karmaoui, Siham Zerouali
• Drought and desertification, exploring the connections under the young eyes in Moroccan pre-Sahara, Draa Valleys / Ahmed Karmaoui, Siham Zerouali
• Ecological and social drivers of ecosystem vulnerability in Oasis Biome, Morocco / Ahmed Karmaoui
• Biodiversity informatics management initiative in consonance with conservation and ecosystem services in climate change adaptation / Dipankar Saha, R.K. Bhatt
• Climate change, ecosystem services and food security / Samreen Siddiqui

Ecosystems provide services that are crucial and beneficial to the human population. The management and conservation of these services can assure the wellbeing of the local population. Climate Change and Its Impact on Ecosystem Services and Biodiversity in Arid and Semi-Arid Zones is an essential reference source that studies the effects of climate change on biodiversity and ecosystem services in dry regions and examines various strategic local, national, and international policy developments to help overcome these impacts. Featuring research on topics such as poverty reduction, climate change, and adaption policies, this book is ideally designed for environmentalists, policymakers, government officials, academicians, researchers, and technology developers who want to improve their understanding of climate change impact, vulnerability, and sustainability, and the strategic role of adaptation and mitigation.
(source: Nielsen Book Data)

• I Preliminaries and Tools
• 1: Introduction
• 2: Symmetries of Space-Time
• 3: Relativistic Wave Equations
• 4: The Hydrogen Atom and Positronium
• 5: The Quark Model
• 6: Detectors of Elementary Particles
• 7: Tools for Calculation II The Strong Interaction
• 8: Electron-Positron Annihilation
• 9: Deep Inelastic Electron Scattering
• 10: The Gluon
• 11: Quantum Chromodynamics
• 12: Partons and Jets
• 13: QCD at Hadron Colliders
• 14: Chiral Symmetry III The Weak Interaction
• 15: The Current-Current Model of the Weak Interaction
• 16: Gauge Theories with Spontaneous Symmetry Breaking
• 17: The W and Z Bosons
• 18: Quark Mixing Angles and Weak Decays
• 19: CP Violation
• 20: Neutrino Masses and Mixings
• 21: The Higgs Boson
• 22: Epilogue.
• (source: Nielsen Book Data)

The purpose of this textbook is to explain the Standard Model of particle physics to a student with an undergraduate preparation in physics. Today we can claim to have a fundamental picture of the strong and weak subnuclear forces. Through an interplay between theory and experiment, we have learned the basic equations through which these forces operate, and we have tested these equations against observations at particle accelerators. The story is beautiful and full of surprises. Using a simplified presentation that does not assume prior knowledge of quantum field theory, this book begins from basic concepts of special relativity and quantum mechanics, describes the key experiments that have clarified the structure of elementary particle interactions, introduces the crucial theoretical concepts, and builds up to the full description of elementary particle interactions as we know them today.
(source: Nielsen Book Data)

• Introduction Preliminaries A $2\times 2$ matrix trick Ultrapowers of trivial $\mathrm W^*$-bundles Property (SI) and its consequences Unitary equivalence of totally full positive elements $2$-coloured equivalence Nuclear dimension and decomposition rank Quasidiagonal traces Kirchberg algebras Addendum Bibliography.
• (source: Nielsen Book Data)

The authors introduce the concept of finitely coloured equivalence for unital $^*$-homomorphisms between $\mathrm C^*$-algebras, for which unitary equivalence is the $1$-coloured case. They use this notion to classify $^*$-homomorphisms from separable, unital, nuclear $\mathrm C^*$-algebras into ultrapowers of simple, unital, nuclear, $\mathcal Z$-stable $\mathrm C^*$-algebras with compact extremal trace space up to $2$-coloured equivalence by their behaviour on traces; this is based on a $1$-coloured classification theorem for certain order zero maps, also in terms of tracial data. As an application the authors calculate the nuclear dimension of non-AF, simple, separable, unital, nuclear, $\mathcal Z$-stable $\mathrm C^*$-algebras with compact extremal trace space: it is 1. In the case that the extremal trace space also has finite topological covering dimension, this confirms the remaining open implication of the Toms-Winter conjecture. Inspired by homotopy-rigidity theorems in geometry and topology, the authors derive a ``homotopy equivalence implies isomorphism'' result for large classes of $\mathrm C^*$-algebras with finite nuclear dimension.
(source: Nielsen Book Data)

• A first look at the mass-critical problem
• The cubic NLS in dimensions three and four
• The energy-critical problem in higher dimensions
• Mass-critical NLS problem in higher dimensions
• Low-dimensional well-posedness results.

• Introduction Preliminaries Meromorphic continuation of the resolvent Boundary layer operators Dynamical resonance free regions Existence of resonances for the Delta potential Appendix A. Model cases Appendix B. Semiclassical intersecting Lagrangian distributions Appendix C. The semiclassical Melrose-Taylor parametrix Bibliography.
• (source: Nielsen Book Data)

The author studies high energy resonances for the operators $-\Delta_{\partial\Omega, \delta}:=-\Delta \delta_{\partial\Omega}\otimes V\quad \textrm{and}\quad -\Delta_{\partial\Omega, \delta'}:=-\Delta \delta_{\partial\Omega}'\otimes V\partial_\nu$ where $\Omega\subset{\mathbb{R}}^{d}$ is strictly convex with smooth boundary, $V:L^{2}(\partial\Omega)\to L^{2}(\partial\Omega)$ may depend on frequency, and $\delta_{\partial\Omega}$ is the surface measure on $\partial\Omega$.
(source: Nielsen Book Data)

• Introduction Preliminary Remarks Step I Step II Step III Step IV Induction Isoenergetic Sets. Generalized Eigenfunctions of $H$ Proof of Absolute Continuity of the Spectrum Appendices List of main notations Bibliography.
• (source: Nielsen Book Data)

The authors consider a Schrodinger operator $H=-\Delta +V(\vec x)$ in dimension two with a quasi-periodic potential $V(\vec x)$. They prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties. First, the eigenfunctions are close to plane waves $e^i\langle \vec \varkappa , \vec x\rangle $ in the high energy region. Second, the isoenergetic curves in the space of momenta $\vec \varkappa $ corresponding to these eigenfunctions have the form of slightly distorted circles with holes (Cantor type structure). A new method of multiscale analysis in the momentum space is developed to prove these results. The result is based on a previous paper on the quasiperiodic polyharmonic operator $(-\Delta )^l+V(\vec x)$, $l>1$. Here the authors address technical complications arising in the case $l=1$. However, this text is self-contained and can be read without familiarity with the previous paper.
(source: Nielsen Book Data)

• Classical models of light
• Photons : the motivation to go beyond classical optics
• Quantum odels of light
• Basic optical components
• Lasers and amplifiers
• Photon generation and detection
• Quantum noise : basic measurements and techniques
• Squeezed light
• Applications of quantum light
• QND
• Fundamental tests of quantum mechanics --Quantum information
• The future : from Q-demonstrations to Q-technologies
• Appendix A : List of quantum operators, states, and functions
• Appendix B: Calculation of the quantum properties of a feedback loop
• Appendix C : Detection of signal and noise with an ESA reference
• Appendix D : An example of analogue processing of photocurrents
• Appendix E : Symbols and abbreviations

Provides fully updated coverage of new experiments in quantum optics This fully revised and expanded edition of a well-established textbook on experiments on quantum optics covers new concepts, results, procedures, and developments in state-of-the-art experiments. It starts with the basic building blocks and ideas of quantum optics, then moves on to detailed procedures and new techniques for each experiment. Focusing on metrology, communications, and quantum logic, this new edition also places more emphasis on single photon technology and hybrid detection. In addition, it offers end-of-chapter summaries and full problem sets throughout. Beginning with an introduction to the subject, A Guide to Experiments in Quantum Optics, 3rd Edition presents readers with chapters on classical models of light, photons, quantum models of light, as well as basic optical components. It goes on to give readers full coverage of lasers and amplifiers, and examines numerous photodetection techniques being used today. Other chapters examine quantum noise, squeezing experiments, the application of squeezed light, and fundamental tests of quantum mechanics. The book finishes with a section on quantum information before summarizing of the contents and offering an outlook on the future of the field. -Provides all new updates to the field of quantum optics, covering the building blocks, models and concepts, latest results, detailed procedures, and modern experiments -Places emphasis on three major goals: metrology, communications, and quantum logic -Presents fundamental tests of quantum mechanics (Schrodinger Kitten, multimode entanglement, photon systems as quantum emulators), and introduces the density function -Includes new trends and technologies in quantum optics and photodetection, new results in sensing and metrology, and more coverage of quantum gates and logic, cluster states, waveguides for multimodes, discord and other quantum measures, and quantum control -Offers end of chapter summaries and problem sets as new features A Guide to Experiments in Quantum Optics, 3rd Edition is an ideal book for professionals, and graduate and upper level students in physics and engineering science.
(source: Nielsen Book Data)

• Introduction
• The Direct Scattering Problem
• The Inverse Scattering Problem
• The Helmholtz Equation
• Acoustic Waves
• Green's Theorem and Formula
• Spherical Harmonics
• Spherical Bessel Functions
• The Far Field Pattern
• Direct Acoustic Obstacle Scattering
• Single- and Double-Layer Potentials
• Scattering from a Sound-Soft Obstacle
• Impedance Boundary Conditions
• Herglotz Wave Functions and the Far Field Operator
• The Two-Dimensional Case
• On the Numerical Solution in R2
• On the Numerical Solution in R3
• Ill-Posed Problems
• The Concept of Ill-Posedness
• Regularization Methods
• Singular Value Decomposition
• Tikhonov Regularization
• Nonlinear Operators
• Inverse Acoustic Obstacle Scattering
• Uniqueness
• Physical Optics Approximation
• Continuity and Differentiability of the Far Field Mapping
• Iterative Solution Methods
• Decomposition Methods
• Sampling Methods
• The Maxwell Equations
• Electromagnetic Waves
• Green's Theorem and Formula
• Vector Potentials
• Scattering from a Perfect Conductor
• Vector Wave Functions
• Herglotz Pairs and the Far Field Operator
• Inverse Electromagnetic Obstacle Scattering
• Uniqueness
• Continuity and Differentiability of the Far Field Mapping
• Iterative Solution Methods
• Decomposition Methods
• Sampling Methods
• Acoustic Waves in an Inhomogeneous Medium
• Physical Background
• The Lippmann-Schwinger Equation
• The Unique Continuation Principle
• The Far Field Pattern
• The Analytic Fredholm Theory
• Transmission Eigenvalues
• Numerical Methods
• Electromagnetic Waves in an Inhomogeneous Medium
• Physical Background
• Existence and Uniqueness
• The Far Field Patterns
• The Spherically Stratified Dielectric Medium
• The Exterior Impedance Boundary Value Problem
• Transmission Eigenvalues
• Existence of Transmission Eigenvalues
• Integral Equation Methods for Transmission Eigenvalues
• Complex Transmission Eigenvalues for Spherically Stratified Media
• The Inverse Spectral Problem for Transmission Eigenvalues
• Modified Transmission Eigenvalues and Their Use as Target Signatures
• The Inverse Medium Problem
• The Inverse Medium Problem for Acoustic Waves
• Uniqueness
• Iterative Solution Methods
• Decomposition Methods
• Sampling Methods
• The Inverse Medium Problem for Electromagnetic Waves
• Remarks on Anisotropic Media
• Numerical Examples
• References
• Index

The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging and geophysical exploration. This text is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves.
(source: Nielsen Book Data)
The inverse scattering problem is central to many areas of science and technology such as radar and sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this third edition, new sections have been added on the linear sampling and factorization methods for solving the inverse scattering problem as well as expanded treatments of iteration methods and uniqueness theorems for the inverse obstacle problem. These additions have in turn required an expanded presentation of both transmission eigenvalues and boundary integral equations in Sobolev spaces. As in the previous editions, emphasis has been given to simplicity over generality thus providing the reader with an accessible introduction to the field of inverse scattering theory. Review of earlier editions: "Colton and Kress have written a scholarly, state of the art account of their view of direct and inverse scattering. The book is a pleasure to read as a graduate text or to dip into at leisure. It suggests a number of open problems and will be a source of inspiration for many years to come." SIAM Review, September 1994 "This book should be on the desk of any researcher, any student, any teacher interested in scattering theory." Mathematical Intelligencer, June 1994.
(source: Nielsen Book Data)
The inverse scattering problem is central to many areas of science and technology such as radar, sonar, medical imaging, geophysical exploration and nondestructive testing. This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. In this fourth edition, a number of significant additions have been made including a new chapter on transmission eigenvalues and a new section on the impedance boundary condition where particular attention has been made to the generalized impedance boundary condition and to nonlocal impedance boundary conditions. Brief discussions on the generalized linear sampling method, the method of recursive linearization, anisotropic media and the use of target signatures in inverse scattering theory have also been added.
(source: Nielsen Book Data)
This book is devoted to the mathematical and numerical analysis of the inverse scattering problem for acoustic and electromagnetic waves. The second edition includes material on Newton's method for the inverse obstacle problem, an elegant proof of uniqueness for the inverse medium problem, a discussion of the spectral theory of the far field operator and a method for determining the support of an inhomogeneous medium from far field data.
(source: Nielsen Book Data)

• Fourier series Fourier transform Convolution Distributions and their Fourier transforms $\delta$ hard at work Sampling and interpolation Discrete Fourier transform Linear time-invariant systems $n$-Dimensional Fourier transform A list of mathematical topics that are fair game Complex numbers and complex exponentials Geometric sums Index.
• (source: Nielsen Book Data)

This book is derived from lecture notes for a course on Fourier analysis for engineering and science students at the advanced undergraduate or beginning graduate level. Beyond teaching specific topics and techniques--all of which are important in many areas of engineering and science--the author's goal is to help engineering and science students cultivate more advanced mathematical know-how and increase confidence in learning and using mathematics, as well as appreciate the coherence of the subject. He promises the readers a little magic on every page. The section headings are all recognizable to mathematicians, but the arrangement and emphasis are directed toward students from other disciplines. The material also serves as a foundation for advanced courses in signal processing and imaging. There are over 200 problems, many of which are oriented to applications, and a number use standard software. An unusual feature for courses meant for engineers is a more detailed and accessible treatment of distributions and the generalized Fourier transform. There is also more coverage of higher-dimensional phenomena than is found in most books at this level.
(source: Nielsen Book Data)

• List of Figures xiii List of Tables xxv Preface xxvii Acknowledgments xxxi 1 Introduction to Rotational, Fine, and Hyperfine Structure of Molecular Radicals 1 1.1 Why Molecules are Complex 1 1.2 Separation of Scales 3 1.2.1 Electronic Energy 5 1.2.2 Vibrational Energy 10 1.2.3 Rotational and Fine Structure 14 1.3 Rotation of a Molecule 17 1.4 Hund's Cases 21 1.4.1 Hund's Coupling Case (a) 21 1.4.2 Hund's Coupling Case (b) 22 1.4.3 Hund's Coupling Case (c) 23 1.5 Parity of Molecular States 23 1.6 General Notation for Molecular States 27 1.7 Hyperfine Structure of Molecules 28 1.7.1 Magnetic Interactions with Nuclei 28 1.7.2 Fermi Contact Interaction 29 1.7.3 Long-Range Magnetic Dipole Interaction 30 1.7.4 Electric Quadrupole Hyperfine Interaction 31 Exercises 31 2 DCStarkEffect 35 2.1 Electric Field Perturbations 35 2.2 Electric Dipole Moment 37 2.3 Linear and Quadratic Stark Shifts 40 2.4 Stark Shifts of Rotational Levels 42 2.4.1 Molecules in a 1 Electronic State 42 2.4.2 Molecules in a 2 Electronic State 46 2.4.3 Molecules in a 3 Electronic State 48 2.4.4 Molecules in a 1 Electronic State - -Doubling 51 2.4.5 Molecules in a 2 Electronic State 54 Exercises 56 3 Zeeman Effect 59 3.1 The Electron Spin 59 3.1.1 The Dirac Equation 60 3.2 Zeeman Energy of a Moving Electron 63 3.3 Magnetic Dipole Moment 64 3.4 Zeeman Operator in the Molecule-Fixed Frame 66 3.5 Zeeman Shifts of Rotational Levels 67 3.5.1 Molecules in a 2 State 67 3.5.2 Molecules in a 2 Electronic State 71 3.5.3 Isolated States 74 3.6 Nuclear Zeeman Effect 75 3.6.1 Zeeman Effect in a 1 Molecule 76 Exercises 78 4 ACStarkEffect 81 4.1 Periodic Hamiltonians 82 4.2 The Floquet Theory 84 4.2.1 Floquet Matrix 88 4.2.2 Time Evolution Operator 89 4.2.3 Brief Summary of Floquet Theory Results 90 4.3 Two-Mode Floquet Theory 92 4.4 RotatingWave Approximation 94 4.5 Dynamic Dipole Polarizability 96 4.5.1 Polarizability Tensor 97 4.5.2 Dipole Polarizability of a DiatomicMolecule 99 4.5.3 Rotational vs Vibrational vs Electronic Polarizability 101 4.6 Molecules in an Off-Resonant Laser Field 104 4.7 Molecules in a Microwave Field 107 4.8 Molecules in a Quantized Field 109 4.8.1 Field Quantization 109 4.8.2 Interaction of Molecules with Quantized Field 116 4.8.3 Quantized Field vs Floquet Theory 117 Exercises 118 5 Molecular Rotations Under Control 121 5.1 Orientation and Alignment 122 5.1.1 OrientingMolecular Axis in Laboratory Frame 123 5.1.2 Quantum Pendulum 126 5.1.3 Pendular States of Molecules 129 5.1.4 Alignment of Molecules by Intense Laser Fields 131 5.2 Molecular Centrifuge 136 5.3 OrientingMolecules Matters -Which Side Chemistry 140 5.4 Conclusion 142 Exercises 142 6 External Field Traps 145 6.1 Deflection and Focusing of Molecular Beams 146 6.2 Electric (and Magnetic) Slowing of Molecular Beams 151 6.3 Earnshaw'sTheorem 155 6.4 Electric Traps 158 6.5 Magnetic Traps 162 6.6 Optical Dipole Trap 165 6.7 Microwave Trap 167 6.8 Optical Lattices 168 6.9 Some Applications of External Field Traps 171 Exercises 173 7 Molecules in Superimposed Fields 175 7.1 Effects of Combined DC Electric andMagnetic Fields 175 7.1.1 Linear Stark Effect at Low Fields 175 7.1.2 Imaging of Radio-Frequency Fields 178 7.2 Effects of Combined DC and AC Electric Fields 181 7.2.1 Enhancement of Orientation by Laser Fields 181 7.2.2 Tug ofWar Between DC and Microwave Fields 182 8 Molecular Collisions in External Fields 187 8.1 Coupled-ChannelTheory of Molecular Collisions 188 8.1.1 A Very General Formulation 188 8.1.2 Boundary Conditions 191 8.1.3 Scattering Amplitude 194 8.1.4 Scattering Cross
• Section 197 8.1.5 Scattering of Identical Molecules 200 8.1.6 Numerical Integration of Coupled-Channel Equations 204 8.2 Interactions with External Fields 208 8.2.1 Coupled-Channel Equations in Arbitrary Basis 208 8.2.2 External Field Couplings 209 8.3 The Arthurs-Dalgarno Representation 211 8.4 Scattering Rates 214 9 Matrix Elements of Collision Hamiltonians 217 9.1 Wigner-EckartTheorem 218 9.2 Spherical Tensor Contraction 220 9.3 Collisions in a Magnetic Field 221 9.3.1 Collisions of 1S-Atoms with 2 -Molecules 221 9.3.2 Collisions of 1S-Atoms with 3 -Molecules 225 9.4 Collisions in an Electric Field 229 9.4.1 Collisions of 2 Molecules with 1S Atoms 229 9.5 Atom-Molecule Collisions in a Microwave Field 232 9.6 Total Angular Momentum Representation for Collisions in Fields 234 10 Field-Induced Scattering Resonances 239 10.1 Feshbach vs Shape Resonances 239 10.2 The Green's Operator in Scattering Theory 242 10.3 Feshbach Projection Operators 243 10.4 Resonant Scattering 246 10.5 Calculation of Resonance Locations andWidths 249 10.5.1 Single Open Channel 249 10.5.2 Multiple Open Channels 249 10.6 Locating Field-Induced Resonances 252 11 Field Control of Molecular Collisions 257 11.1 Why to Control Molecular Collisions 257 11.2 Molecular Collisions are Difficult to Control 259 11.3 General Mechanisms for External Field Control 261 11.4 Resonant Scattering 261 11.5 Zeeman and Stark Relaxation at Zero Collision Energy 264 11.6 Effect of Parity Breaking in Combined Fields 269 11.7 Differential Scattering in Electromagnetic Fields 271 11.8 Collisions in Restricted Geometries 272 11.8.1 Threshold Scattering of Molecules in Two Dimensions 276 11.8.2 Collisions in a Quasi-Two-Dimensional Geometry 280 12 Ultracold Controlled Chemistry 283 12.1 Can Chemistry Happen at Zero Kelvin? 284 12.2 Ultracold Stereodynamics 287 12.3 Molecular Beams Under Control 289 12.4 Reactions in Magnetic Traps 289 12.5 Ultracold Chemistry - The Why and What's Next? 291 12.5.1 Practical Importance of Ultracold Chemistry? 291 12.5.2 Fundamental Importance of Ultracold Controlled Chemistry 293 12.5.3 A Brief Outlook 294 A Unit Conversion Factors 297 B Addition of AngularMomenta 299 B.1 The Clebsch-Gordan Coefficients 301 B.2 TheWigner 3j-Symbols 303 B.3 The Raising and Lowering Operators 304 C Direction Cosine Matrix 307 D Wigner D-Functions 309 D.1 Matrix elements involving D-functions 311 E Spherical tensors 315 E.1 Scalar and Vector Products of Vectors in Spherical Basis 317 E.2 Scalar and Tensor Products of Spherical Tensors 318 References 321 Index 347.
• (source: Nielsen Book Data)

A tutorial for calculating the response of molecules to electric and magnetic fields with examples from research in ultracold physics, controlled chemistry, and molecular collisions in fields Molecules in Electromagnetic Fields is intended to serve as a tutorial for students beginning research, theoretical or experimental, in an area related to molecular physics. The author-a noted expert in the field-offers a systematic discussion of the effects of static and dynamic electric and magnetic fields on the rotational, fine, and hyperfine structure of molecules. The book illustrates how the concepts developed in ultracold physics research have led to what may be the beginning of controlled chemistry in the fully quantum regime. Offering a glimpse of the current state of the art research, this book suggests future research avenues for ultracold chemistry. The text describes theories needed to understand recent exciting developments in the research on trapping molecules, guiding molecular beams, laser control of molecular rotations, and external field control of microscopic intermolecular interactions. In addition, the author presents the description of scattering theory for molecules in electromagnetic fields and offers practical advice for students working on various aspects of molecular interactions. This important text: Offers information on theeffects of electromagnetic fields on the structure of molecular energy levels Includes thorough descriptions of the most useful theories for ultracold molecule researchers Presents a wealth of illustrative examples from recent experimental and theoretical work Contains helpful exercises that help to reinforce concepts presented throughout text Written for senior undergraduate and graduate students, professors, researchers, physicists, physical chemists, and chemical physicists, Molecules in Electromagnetic Fields is an interdisciplinary text describing theories and examples from the core of contemporary molecular physics. .
(source: Nielsen Book Data)
This book introduces the reader to the quantum theories needed to describe the interactions of diatomic molecules with electromagnetic fields and systematically discusses the effects of static and dynamic electric and magnetic fields on the rotational, fine, and hyperfine structure of molecules. It illustrates how the concepts developed in ultracold physics research have lead to what may be the beginning of controlled chemistry in the fully quantum regime. The theories described are applied to discuss examples from research on trapping molecules in electromagnetic fields, laser control of molecular rotations and external field control of microscopic intermolecular interactions. The book presents the description of scattering theory for molecules in electromagnetic fields and is written to be a practical guide for students working on various aspects of molecular interactions.
(source: Nielsen Book Data)

Although hints of a crisis appeared as early as the 1570s, the temperature by the end of the sixteenth century plummeted so drastically that Mediterranean harbors were covered with ice, birds literally dropped out of the sky, and "frost fairs" were erected on a frozen Thames-with kiosks, taverns, and even brothels that become a semi-permanent part of the city. Recounting the deep legacy and far-ranging consequences of this "Little Ice Age, " acclaimed historian Philipp Blom reveals how the European landscape had suddenly, but ineradicably, changed by the mid-seventeenth century. While apocalyptic weather patterns destroyed entire harvests and incited mass migrations, they gave rise to the growth of European cities, the emergence of early capitalism, and the vigorous stirrings of the Enlightenment. A timely examination of how a society responds to profound and unexpected change, Nature's Mutiny will transform the way we think about climate change in the twenty-first century and beyond.
(source: Nielsen Book Data)

• Preface
• Making the impossible possible. Impossible! ; The Penrose puzzle ; Finding the loophole ; A tale of two laboratories ; Something exciting to show you ; Perfectly impossible
• The quest begins. Did nature beat us? ; Luca ; Quasi-happy new year ; When you say impossible ; Blue team vs. red team ; A capricious if not overtly malicious God ; The secret secret diary ; Valery Kryachko ; Something rare surrounding something impossible ; Icosahedrite
• Kamchatka or bust. Lost ; Found ; Ninety-nine percent ; Beating the odds ; L'uomo dei miracoli ; Nature's secret.

"One of the most fascinating scientific detective stories of the last fifty years, an exciting quest for a new form of matter. The Second Kind of Impossible reads like James Gleick's Chaos combined with an Indiana Jones adventure"-- Provided by publisher.
"One or the most stunning scientific detective stories of the last fifty years--like James Gleick's Chaos wrapped in an Indiana Jones adventure. When world-renowned physicist Paul Steinhardt began his career in the 1980s, scientists thought they had identified all the possible types of matter. The issue had been settled science for centuries. But when Steinhardt pursued a wild fantasy he first imagined as a curious teenager, it led to a radical new theory, predicting an astonishing form of matter that broke all the established rules. The breakthrough would launch him on a thirty-five-year quest to prove the substance's existence in the natural world. [This] is the untold story of Steinhardt's odyssey and a candid account of the brilliant, and often bruising, battles that take place behind the scenes of scientific progress. Steinhardt and his stellar team of researchers encounter international smugglers, corrupt scientists, secret diaries, fraudulent traders, political intrigue, and Russian security agents. Their search culminates in a daring expedition to one of the most inhospitable regions on Earth, pursuing tiny fragments of a meteorite forged at the birth of the solar system. Steinhardt and his team chart a new direction in science. They not only change our ideas about the fundamentals of matter but also reveal new truths about the processes that shaped our solar system. The underlying science is deceptively simple, unexpectedly beautiful, and nothing short of revolutionary. Steinhardt's firsthand account is a scientific thriller of the first order."--Dust jacket.

• Classical string theory
• Quantization of bosonic strings
• Conformal field theory
• Scattering amplitudes and vertex operators
• Strings in background fields
• Superstrings and supersymmetry
• D-branes
• Compactification and supersymmetry breaking
• Loop corrections to string effective couplings
• Duality connections and nonperturbative effects
• Compactifications with fluxes
• Black holes and entropy in string theory
• The bulk/boundary (holographic) correspondence
• Applications of the holographic correspondence
• String theory and matrix models
• Appendix A : Two-dimensional complex geometry
• Appendix B : Differential forms
• Appendix C : Conformal transformations and curvature
• Appendix D: Theta and other elliptic functions
• Appendix E : Toroidal lattice sums
• Appendix F : Toroidal Kaluza-Klein reduction
• Appendix G : The Reissner-Nordström black hole
• Appendix H : Electric-magnetic duality in D = 4
• Appendix I : Supersymmetric actions in ten and eleven dimensions
• Appendix J : N = 1,2, four-dimensional supergravity coupled to matter
• Appendix K : BPS multiplets in four dimensions
• Appendix L : The geometry of anti-de Sitter space

The essential introduction to modern string theory-now fully expanded and revised String Theory in a Nutshell is the definitive introduction to modern string theory. Written by one of the world's leading authorities on the subject, this concise and accessible book starts with basic definitions and guides readers from classic topics to the most exciting frontiers of research today. It covers perturbative string theory, the unity of string interactions, black holes and their microscopic entropy, the AdS/CFT correspondence and its applications, matrix model tools for string theory, and more. It also includes 600 exercises and serves as a self-contained guide to the literature. This fully updated edition features an entirely new chapter on flux compactifications in string theory, and the chapter on AdS/CFT has been substantially expanded by adding many applications to diverse topics. In addition, the discussion of conformal field theory has been extensively revised to make it more student-friendly. The essential one-volume reference for students and researchers in theoretical high-energy physics Now fully expanded and revised Provides expanded coverage of AdS/CFT and its applications, namely the holographic renormalization group, holographic theories for Yang-Mills and QCD, nonequilibrium thermal physics, finite density physics, and entanglement entropy Ideal for mathematicians and physicists specializing in theoretical cosmology, QCD, and novel approaches to condensed matter systems An online illustration package is available to professors.
(source: Nielsen Book Data)

• Prologue: listening to the universe
• Mathematics drives away the cloud
• Shining the torch on electricity and magnetism
• Shining the torch on gravity again
• Quantum mathematics
• The long divorce
• Revolution
• Bad company?
• Jokes and magic lead to the string
• Strung together
• Thinking their way to the Millenium
• Diamonds in the rough
• The best possible times.

How math helps us solve the universe's deepest mysteries One of the great insights of science is that the universe has an underlying order. The supreme goal of physicists is to understand this order through laws that describe the behavior of the most basic particles and the forces between them. For centuries, we have searched for these laws by studying the results of experiments. Since the 1970s, however, experiments at the world's most powerful atom-smashers have offered few new clues. So some of the world's leading physicists have looked to a different source of insight: modern mathematics. These physicists are sometimes accused of doing 'fairy-tale physics', unrelated to the real world. But in The Universe Speaks in Numbers, award-winning science writer and biographer Farmelo argues that the physics they are doing is based squarely on the well-established principles of quantum theory and relativity, and part of a tradition dating back to Isaac Newton. With unprecedented access to some of the world's greatest scientific minds, Farmelo offers a vivid, behind-the-scenes account of the blossoming relationship between mathematics and physics and the research that could revolutionize our understanding of reality. A masterful account of the some of the most groundbreaking ideas in physics in the past four decades. The Universe Speaks in Numbers is essential reading for anyone interested in the quest to discover the fundamental laws of nature.
(source: Nielsen Book Data)

• Calculation
• Calculating the weather
• The forecast factories
• Observation
• The weather on earth
• Looking down
• Going around
• Blasting off
• Simulation
• The mountaintop
• The euro
• The app
• The good forecast
• Preservation
• The weather diplomats.

"From the acclaimed author of Tubes, a lively and surprising tour of the infrastructure behind the weather forecast, the people who built it, and what it reveals about our climate and our planet. The weather is the foundation of our daily lives. It's a staple of small talk, the app on our smartphones, and often the first thing we check each morning. Yet behind these quotidian interactions is one of the most expansive machines human beings have ever constructed -- a triumph of science, technology and global cooperation. But what is this 'weather machine' and who created it? In The Weather Machine, Andrew Blum takes readers on a fascinating journey through an everyday miracle. In a quest to understand how the forecast works, he visits old weather stations and watches new satellites blast off. He follows the dogged efforts of scientists to create a supercomputer model of the atmosphere and traces the surprising history of the algorithms that power their work. He discovers that we have quietly entered a golden age of meteorology -- our tools allow us to predict weather more accurately than ever, and yet we haven't learned to trust them, nor can we guarantee the fragile international alliances that allow our modern weather machine to exist. Written with the sharp wit and infectious curiosity Andrew Blum is known for, The Weather Machine pulls back the curtain on a universal part of our everyday lives, illuminating our relationships with technology, the planet, and the global community" -- Jacket.

• 1. Introduction to modern methods for classical and quantum fields in general relativity Thierry Daude, Dietrich Hafner and Jean-Philippe Nicolas
• 2. Geometry of black hole spacetimes Lars Andersson, Thomas Backdahl and Pieter Blue
• 3. An introduction to confirmal geometry and tractor calculus, with a view to applications in general relativity Sean N. Curry and A. Rod Gover
• 4. An introduction to quantum field theory on curved spacetimes Christian Gerard
• 5. A minicourse on microlocal analysis for wave propagation Andras Vasy.
• (source: Nielsen Book Data)

This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic analysis of classical and quantum fields in general relativity. Accessible to graduate students, these notes gather results that were not previously available in textbooks or monographs and will be of wider interest to researchers in general relativity. The topics of these mini courses are: the geometry of black hole spacetimes; an introduction to quantum field theory on curved spacetimes; conformal geometry and tractor calculus; and microlocal analysis for wave propagation.
(source: Nielsen Book Data)

Until now, popular science has relegated the atom to a supporting role in defining the different chemical elements of the periodic table. This bold new title places its subject center stage, shining the spotlight directly onto the structure and properties of this tiniest amount of anything it is possible to identify. The book covers a huge range of topics, including the development of scientific thinking about the atom, the basic structure of the atom, how the interactions between atoms account for the familiar properties of everyday materials; the power and mystery of the atomic nucleus, and what the mysterious quantum realm of subatomic particles and their interactions can tell us about the very nature of reality. Sparkling text banishes an outdated world of dull chemistry, as it brightly introduces the reader to what everything is made of and how it all works, on the most fundamental level.
(source: Nielsen Book Data)

• Introduction.- The Concept of the Atom.- Development of Quantum Physics.- Basic Concepts of Quantum Mechanics.- The Hydrogen Atom.- Atoms with More Than One Electron.- Emission and Absorption of Electromagnetic Radiation by Atoms.- Lasers.- Diatomic Molecules.- Polyatomic Molecules.- Experimental Techniques in Atomic and Molecular Physics.- Modern Developments in Atomic and Molecular Physics.- Chronological Table for the Development of Atomic and Molecular Physics.- Solutions to the Exercises.
• (source: Nielsen Book Data)

This introduction to Atomic and Molecular Physics explains how our present model of atoms and molecules has been developed over the last two centuries both by many experimental discoveries and, from the theoretical side, by the introduction of quantum physics to the adequate description of micro-particles. It illustrates the wave model of particles by many examples and shows the limits of classical description. The interaction of electromagnetic radiation with atoms and molecules and its potential for spectroscopy is outlined in more detail and in particular lasers as modern spectroscopic tools are discussed more thoroughly. Many examples and problems with solutions are offered to encourage readers to actively engage in applying and adapting the fundamental physics presented in this textbook to specific situations. Completely revised third edition with new sections covering all actual developments, like photonics, ultrashort lasers, ultraprecise frequency combs, free electron lasers, cooling and trapping of atoms, quantum optics and quantum information.
(source: Nielsen Book Data)

• Beginnings
• It's not what it used to be
• The Arctic stirs
• Unaami
• Epiphany
• Rude awakenings
• Looking ahead.

An insider account of how researchers unraveled the mystery of the thawing Arctic In the 1990s, researchers in the Arctic noticed that floating summer sea ice had begun receding. This was accompanied by shifts in ocean circulation and unexpected changes in weather patterns throughout the world. The Arctic's perennially frozen ground, known as permafrost, was warming, and treeless tundra was being overtaken by shrubs. What was going on? Brave New Arctic is Mark Serreze's riveting firsthand account of how scientists from around the globe came together to find answers. In a sweeping tale of discovery spanning three decades, Serreze describes how puzzlement turned to concern and astonishment as researchers came to understand that the Arctic of old was quickly disappearing--with potentially devastating implications for the entire planet. Serreze is a world-renowned Arctic geographer and climatologist who has conducted fieldwork on ice caps, glaciers, sea ice, and tundra in the Canadian and Alaskan Arctic. In this must-read book, he blends invaluable insights from his own career with those of other pioneering scientists who, together, ushered in an exciting new age of Arctic exploration. Along the way, he accessibly describes the cutting-edge science that led to the alarming conclusion that the Arctic is rapidly thawing due to climate change, that humans are to blame, and that the global consequences are immense. A gripping scientific adventure story, Brave New Arctic shows how the Arctic's extraordinary transformation serves as a harbinger of things to come if we fail to meet the challenge posed by a warming Earth.
(source: Nielsen Book Data)

• A Neurologist Walks in Princeton April 18, 1955 What the Neuropathologist Knew ... And Didn't Know The Lost Decades (1955-1985), the Cider Box, and the Microscope The Exceptional Brain(s) of Albert Einstein How Does a Genius Think? The Pursuit of Genius Where Do We Go From Here? (And Where Have We Been?).
• (source: Nielsen Book Data)

Albert Einstein remains the quintessential icon of modern genius. Like Newton and many others, his seminal work in physics includes the Theory of General Relativity and perhaps the most famous equation of all time: E = mc2. Following his death in 1955, Einstein's brain was removed and preserved, but has never been fully or systematically studied. In fact, the sections are not even all in one place, and some are mysteriously unaccounted for! In this compelling tale, Frederick E. Lepore delves into the strange, elusive afterlife of Einstein's brain and what it represents for brain and/or intelligence studies. This "biography of a brain" explores how Einstein's brain anatomy was truly exceptional, and how "found" photographs of his brain-discovered more than a half a century after his death-begin to explain the brain of a genius.
(source: Nielsen Book Data)

• Complex differential equations and geometric structures on curves / Adolfo Guillot
• Blow-up, homotopy and existence for periodic solutions of the planar three-body problem / Richard Montgomery
• A quick view of Lagrangian Floer homology / Andrés Pedroza.

Presenting a selection of recent developments in geometrical problems inspired by the N-body problem, these lecture notes offer a variety of approaches to study them, ranging from variational to dynamical, while developing new insights, making geometrical and topological detours, and providing historical references. A. Guillot's notes aim to describe differential equations in the complex domain, motivated by the evolution of N particles moving on the plane subject to the influence of a magnetic field. Guillot studies such differential equations using different geometric structures on complex curves (in the sense of W. Thurston) in order to find isochronicity conditions. R. Montgomery's notes deal with a version of the planar Newtonian three-body equation. Namely, he investigates the problem of whether every free homotopy class is realized by a periodic geodesic. The solution involves geometry, dynamical systems, and the McGehee blow-up. A novelty of the approach is the use of energy-balance in order to motivate the McGehee transformation. A. Pedroza's notes provide a brief introduction to Lagrangian Floer homology and its relation to the solution of the Arnol'd conjecture on the minimal number of non-degenerate fixed points of a Hamiltonian diffeomorphism.
(source: Nielsen Book Data)

• Chapter 1. Introduction
• Chapter 2. Preliminaries
• Chapter 3. Derivation of the main scalar equation
• Chapter 4. Energy estimates I: high Sobolev estimates
• Chapter 5. Energy estimates II: low frequencies
• Chapter 6. Energy estimates III: Weighted estimates for high frequencies
• Chapter 7. Energy estimates IV: Weighted estimates for low frequencies
• Chapter 8. Decay estimates
• Chapter 9. Proof of Lemma 8.6
• Chapter 10. Modified scattering
• Appendix A. Analysis of symbols
• Appendix B. The Dirichlet-Neumann operator
• Appendix C. Elliptic bounds.

The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the ``quasilinear I-method'') which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called ``division problem''). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.
(source: Nielsen Book Data)

• 1 Preface 2 Introduction
• I Basics of group theory 3 Symmetry operations and transformations of fields 4 Basic abstract group theory 5 Discrete symmetry groups for solid state physics and photonics 6 Representation theory 7 Symmetry in k-space
• II Applications in electronic structure theory 8 Solution of the Schroedinger equation 9 Generalization to include the spin 10 Electronic energy bands
• III Applications in photonics 11 Solution of Maxwell's equations 12 Twodimensional photonic crystals 13 Threedimensional photonic crystals 14 Other Applications
• A Mathematica Package Reference B Connection of the group theory package to MPB and MEEP.
• (source: Nielsen Book Data)

• Preface VII
• 1 Introduction 1 1.1 Symmetries in Solid-State Physics and Photonics 4 1.2 A Basic Example: Symmetries of a Square 6 Part One Basics of Group Theory 9
• 2 Symmetry Operations and Transformations of Fields 11 2.1 Rotations and Translations 11 2.1.1 Rotation Matrices 13 2.1.2 Euler Angles 16 2.1.3 Euler-Rodrigues Parameters and Quaternions 18 2.1.4 Translations and General Transformations 23 2.2 Transformation of Fields 25 2.2.1 Transformation of Scalar Fields and Angular Momentum 26 2.2.2 Transformation of Vector Fields and Total Angular Momentum 27 2.2.3 Spinors 28
• 3 Basics Abstract Group Theory 33 3.1 Basic Definitions 33 3.1.1 Isomorphism and Homomorphism 38 3.2 Structure of Groups 39 3.2.1 Classes 40 3.2.2 Cosets and Normal Divisors 42 3.3 Quotient Groups 46 3.4 Product Groups 48
• 4 Discrete Symmetry Groups in Solid-State Physics and Photonics 51 4.1 Point Groups 52 4.1.1 Notation of Symmetry Elements 52 4.1.2 Classification of Point Groups 56 4.2 Space Groups 59 4.2.1 Lattices, Translation Group 59 4.2.2 Symmorphic and Nonsymmorphic Space Groups 62 4.2.3 Site Symmetry, Wyckoff Positions, and Wigner-Seitz Cell 65 4.3 Color Groups and Magnetic Groups 69 4.3.1 Magnetic Point Groups 69 4.3.2 Magnetic Lattices 72 4.3.3 Magnetic Space Groups 73 4.4 Noncrystallographic Groups, Buckyballs, and Nanotubes 75 4.4.1 Structure and Group Theory of Nanotubes 75 4.4.2 Buckminsterfullerene C60 79
• 5 Representation Theory 83 5.1 Definition of Matrix Representations 84 5.2 Reducible and Irreducible Representations 88 5.2.1 The Orthogonality Theorem for Irreducible Representations 90 5.3 Characters and Character Tables 94 5.3.1 The Orthogonality Theorem for Characters 96 5.3.2 Character Tables 98 5.3.3 Notations of Irreducible Representations 98 5.3.4 Decomposition of Reducible Representations 102 5.4 Projection Operators and Basis Functions of Representations 105 5.5 Direct Product Representations 112 5.6 Wigner-Eckart Theorem 120 5.7 Induced Representations 123
• 6 Symmetry and Representation Theory in k-Space 133 6.1 The Cyclic Born-von Karman Boundary Condition and the Bloch Wave 133 6.2 The Reciprocal Lattice 136 6.3 The Brillouin Zone and the Group of the Wave Vector k 137 6.4 Irreducible Representations of Symmorphic Space Groups 142 6.5 Irreducible Representations of Nonsymmorphic Space Groups 143 Part Two Applications in Electronic Structure Theory 149
• 7 Solution of the SCHROEDINGER Equation 151 7.1 The Schroedinger Equation 151 7.2 The Group of the Schroedinger Equation 153 7.3 Degeneracy of Energy States 154 7.4 Time-Independent Perturbation Theory 157 7.4.1 General Formalism 159 7.4.2 Crystal Field Expansion 160 7.4.3 Crystal Field Operators 164 7.5 Transition Probabilities and Selection Rules 169
• 8 Generalization to Include the Spin 177 8.1 The Pauli Equation 177 8.2 Homomorphism between SU(2) and SO(3) 178 8.3 Transformation of the Spin-Orbit Coupling Operator 180 8.4 The Group of the Pauli Equation and Double Groups 183 8.5 Irreducible Representations of Double Groups 186 8.6 Splitting of Degeneracies by Spin-Orbit Coupling 189 8.7 Time-Reversal Symmetry 193 8.7.1 The Reality of Representations 193 8.7.2 Spin-Independent Theory 194 8.7.3 Spin-Dependent Theory 196
• 9 Electronic Structure Calculations 197 9.1 Solution of the Schroedinger Equation for a Crystal 197 9.2 Symmetry Properties of Energy Bands 198 9.2.1 Degeneracy and Symmetry of Energy Bands 200 9.2.2 Compatibility Relations and Crossing of Bands 201 9.3 Symmetry-Adapted Functions 203 9.3.1 Symmetry-Adapted Plane Waves 203 9.3.2 Localized Orbitals 205 9.4 Construction of Tight-Binding Hamiltonians 210 9.4.1 Hamiltonians in Two-Center Form 212 9.4.2 Hamiltonians in Three-Center Form 216 9.4.3 Inclusion of Spin-Orbit Interaction 224 9.4.4 Tight-Binding Hamiltonians from ab initio Calculations 225 9.5 Hamiltonians Based on Plane Waves 227 9.6 Electronic Energy Bands and Irreducible Representations 230 9.7 Examples and Applications 236 9.7.1 Calculation of Fermi Surfaces 236 9.7.2 Electronic Structure of Carbon Nanotubes 238 9.7.3 Tight-binding Real-Space Calculations 240 9.7.4 Spin-Orbit Coupling in Semiconductors 245 9.7.5 Tight-Binding Models for Oxides 247 Part Three Applications in Photonics 251
• 10 Solution of MAXWELL's Equations 253 10.1 Maxwell's Equations and the Master Equation for Photonic Crystals 254 10.1.1 The Master Equation 254 10.1.2 One- and Two-Dimensional Problems 256 10.2 Group of the Master Equation 257 10.3 Master Equation as an Eigenvalue Problem 259 10.4 Models of the Permittivity 260 10.4.1 Reduced Structure Factors 264 10.4.2 Convergence of the Plane Wave Expansion 266
• 11 Two-Dimensional Photonic Crystals 269 11.1 Photonic Band Structure and Symmetrized Plane Waves 270 11.1.1 Empty Lattice Band Structure and Symmetrized Plane Waves 270 11.1.2 Photonic Band Structures: A First Example 273 11.2 Group Theoretical Classification of Photonic Band Structures 276 11.3 Supercells and Symmetry of Defect Modes 279 11.4 Uncoupled Bands 283
• 12 Three-Dimensional Photonic Crystals 287 12.1 Empty Lattice Bands and Compatibility Relations 287 12.2 An example: Dielectric Spheres in Air 291 12.3 Symmetry-Adapted Vector Spherical Waves 293 Part Four Other Applications 299
• 13 Group Theory of Vibrational Problems 301 13.1 Vibrations of Molecules 301 13.1.1 Permutation, Displacement, and Vector Representation 302 13.1.2 Vibrational Modes of Molecules 305 13.1.3 Infrared and Raman Activity 307 13.2 Lattice Vibrations 310 13.2.1 Direct Calculation of the Dynamical Matrix 312 13.2.2 Dynamical Matrix from Tight-Binding Models 314 13.2.3 Analysis of Zone Center Modes 315
• 14 Landau Theory of Phase Transitions of the Second Kind 319 14.1 Introduction to Landau's Theory of Phase Transitions 320 14.2 Basics of the Group Theoretical Formulation 324 14.3 Examples with GTPack Commands 326 14.3.1 Invariant Polynomials 326 14.3.2 Landau and Lifshitz Criterion 327 Appendix A Spherical Harmonics 331 A.1 Complex Spherical Harmonics 332 A.1.1 Definition of Complex Spherical Harmonics 332 A.1.2 Cartesian Spherical Harmonics 332 A.1.3 Transformation Behavior of Complex Spherical Harmonics 333 A.2 Tesseral Harmonics 334 A.2.1 Definition of Tesseral Harmonics 334 A.2.2 Cartesian Tesseral Harmonics 335 A.2.3 Transformation Behavior of Tesseral Harmonics 336 Appendix B Remarks on Databases 337 B.1 Electronic Structure Databases 337 B.1.1 Tight-Binding Calculations 337 B.1.2 Pseudopotential Calculations 338 B.1.3 Radial Integrals for Crystal Field Parameters 339 B.2 Molecular Databases 339 B.3 Database of Structures 339 Appendix C Use of MPB together with GTPack 341 C.1 Calculation of Band Structure and Density of States 341 C.2 Calculation of Eigenmodes 342 C.3 Comparison of Calculations with MPB and Mathematica 343 Appendix D Technical Remarks on GTPack 345 D.1 Structure of GTPack 345 D.2 Installation of GTPack 346 References 349 Index 359.
• (source: Nielsen Book Data)

While group theory and its application to solid state physics is well established, this textbook raises two completely new aspects. First, it provides a better understanding by focusing on problem solving and making extensive use of Mathematica tools to visualize the concepts. Second, it offers a new tool for the photonics community by transferring the concepts of group theory and its application to photonic crystals. Clearly divided into three parts, the first provides the basics of group theory. Even at this stage, the authors go beyond the widely used standard examples to show the broad field of applications. Part II is devoted to applications in condensed matter physics, i.e. the electronic structure of materials. Combining the application of the computer algebra system Mathematica with pen and paper derivations leads to a better and faster understanding. The exhaustive discussion shows that the basics of group theory can also be applied to a totally different field, as seen in Part III. Here, photonic applications are discussed in parallel to the electronic case, with the focus on photonic crystals in two and three dimensions, as well as being partially expanded to other problems in the field of photonics. The authors have developed Mathematica package GTPack which is available for download from the book's homepage. Analytic considerations, numerical calculations and visualization are carried out using the same software. While the use of the Mathematica tools are demonstrated on elementary examples, they can equally be applied to more complicated tasks resulting from the reader's own research.
(source: Nielsen Book Data)

• The holographic correspondence
• Zero density matter
• Quantum critical transport
• Compressible quantum matter
• Metallic transport without quasiparticles
• Symmetry broken phases
• Further topics
• Connections to experiments.

A comprehensive overview of holographic methods in quantum matter, written by pioneers in the field. This book, written by pioneers in the field, offers a comprehensive overview of holographic methods in quantum matter. It covers influential developments in theoretical physics, making the key concepts accessible to researchers and students in both high energy and condensed matter physics. The book provides a unique combination of theoretical and historical context, technical results, extensive references to the literature, and exercises. It will give readers the ability to understand the important problems in the field, both those that have been solved and those that remain unsolved, and will enable them to engage directly with the current literature. The book describes a particular interface between condensed matter physics, gravitational physics, and string and quantum field theory made possible by holographic duality. The chapters cover such topics as the essential workings of the holographic correspondence; strongly interacting quantum matter at a fixed commensurate density; compressible quantum matter with a variable density; transport in quantum matter; the holographic description of symmetry broken phases; and the relevance of the topics covered to experimental challenges in specific quantum materials. Holographic Quantum Matter promises to be the definitive presentation of this material.
(source: Nielsen Book Data)

• Part I. Theory: 1. The wave function
• 2. Time-independent Schrodinger equation
• 3. Formalism
• 4. Quantum mechanics in three dimensions
• 5. Identical particles
• 6. Symmetry
• Part II. Application: 7. Time-independent perturbation theory
• 8. The variational principle
• 9. The WKB approximation
• 10. Scattering
• 11. Quantum dynamics
• 12. Afterword
• Appendix A. Linear algebra
• Index.
• (source: Nielsen Book Data)

Changes and additions to the new edition of this classic textbook include: new chapter on Symmetries, new problems and examples, improved explanations, more numerical problems to be worked on a computer, new applications to solid state physics, consolidated treatment of time-dependent potentials.
(source: Nielsen Book Data)

• Physical Framework and Models
• Basic Applied Functional Analysis
• Complements of Applied Functional Analysis
• Abstract Mathematical Framework
• Analyses of Exact Problems : First-Order Models
• Analyses of Approximate Models
• Analyses of Exact Problems : Second-Order Models
• Analyses of Time-Harmonic Problems
• Dimensionally Reduced Models : Derivation and Analyses
• Analyses of Coupled Models
• Index of Function Spaces
• References
• Index.

This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well-posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell's equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell's equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.
(source: Nielsen Book Data)

• I. Shock reflection-diffraction, nonlinear conservation laws of mixed type, and von Neumann's conjectures
• Shock reflection-diffraction, nonlinear partial differential equations of mixed type, and free boundary problems
• Mathematical formulations and main theorems
• Main steps and related analysis in the proofs of the main theorems
• II. Elliptic theory and related analysis for shock reflection-diffraction
• Relevant results for nonlinear elliptic equations of second order
• Basic properties of the self-similar potential flow equation
• III. Proofs of the main theorems for the sonic conjecture and related analysis
• Uniform states and normal reflection
• Local theory and von Neumann's conjectures
• Admissible solutions and features of problem 2.6.1
• Uniform estimates for admissible solutions
• Regularity of admissible solutions away from the sonic arc
• Regularity of admissible solutions near the sonic arc
• Iteration set and solvability of the iteration problem
• Iteration map, fixed points, and existence of admissible solutions up to the sonic angle
• Optimal regularity of solutions near the sonic circle
• IV. Subsonic regular reflection-diffraction and global existence of solutions up to the detachment angle
• Regularity of admissible solutions near the sonic arc and the reflection point
• Existence of global regular reflection-diffraction solutions up to the detachment angle
• V. Connections and open problems
• The full Euler equation and the potential flow equation
• Shock reflection-diffraction and new mathematical challenges.

This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development. Shock waves are fundamental in nature. They are governed by the Euler equations or their variants, generally in the form of nonlinear conservation laws--PDEs of divergence form. When a shock hits an obstacle, shock reflection-diffraction configurations take shape. To understand the fundamental issues involved, such as the structure and transition criteria of different configuration patterns, it is essential to establish the global existence, regularity, and structural stability of shock reflection-diffraction solutions. This involves dealing with several core difficulties in the analysis of nonlinear PDEs--mixed type, free boundaries, and corner singularities--that also arise in fundamental problems in diverse areas such as continuum mechanics, differential geometry, mathematical physics, and materials science. Presenting recently developed approaches and techniques, which will be useful for solving problems with similar difficulties, this book opens up new research opportunities.
(source: Nielsen Book Data)

• Part I. Basic Energy Physics and Uses: 1. Introduction
• 2. Mechanical energy
• 3. Electromagnetic energy
• 4. Waves and light
• 5. Thermodynamics I: heat and thermal energy
• 6. Heat transfer
• 7. Introduction to quantum physics
• 8. Thermodynamics II: entropy and temperature
• 9. Energy in matter
• 10. Thermal energy conversion
• 11. Internal combustion engines
• 12. Phase-change energy conversion
• 13. Thermal power and heat extraction cycles
• Part II. Energy Sources: 14. The forces of nature
• 15. Quantum phenomena in energy systems
• 16. An overview of nuclear power
• 17. Structure, properties and decays of nuclei
• 18. Nuclear energy processes: fission and fusion
• 19. Nuclear fission reactors and nuclear fusion experiments
• 20. Ionizing radiation
• 21. Energy in the universe
• 22. Solar energy: solar production and radiation
• 23. Solar energy: solar radiation on Earth
• 24. Solar thermal energy
• 25. Photovoltaic solar cells
• 26. Biological energy
• 27. Ocean energy flow
• 28. Wind: a highly variable resource
• 29. Fluids - the basics
• 30. Wind turbines
• 31. Energy from moving water: hydro, wave, tidal, and marine current power
• 32. Geothermal energy
• 33. Fossil fuels
• Part III. Energy System Issues and Externalities: 34. Energy and climate
• 35. Earth's climate: past, present, and future
• 36. Energy efficiency, conservation, and changing energy sources
• 37. Energy storage
• 38. Electricity generation and transmission.
• (source: Nielsen Book Data)

The Physics of Energy provides a comprehensive and systematic introduction to the scientific principles governing energy sources, uses, and systems. This definitive textbook traces the flow of energy from sources such as solar power, nuclear power, wind power, water power, and fossil fuels through its transformation in devices such as heat engines and electrical generators, to its uses including transportation, heating, cooling, and other applications. The flow of energy through the Earth's atmosphere and oceans, and systems issues including storage, electric grids, and efficiency and conservation are presented in a scientific context along with topics such as radiation from nuclear power and climate change from the use of fossil fuels. Students, scientists, engineers, energy industry professionals, and concerned citizens with some mathematical and scientific background who wish to understand energy systems and issues quantitatively will find this textbook of great interest.
(source: Nielsen Book Data)

• Basic equations for shallow water waves
• Introduction to the KP theory and the t-function
• The real Grassmannians and their parametrizations
• Classification of the KP solitons
• Soliton graphs
• Stability and numerical simulations
• The inverse problem
• The Mach reflection : the miles theory and the higher order KP theory.

Web-like waves, often observed on the surface of shallow water, are examples of nonlinear waves. They are generated by nonlinear interactions among several obliquely propagating solitary waves, also known as solitons. In this book, modern mathematical tools-algebraic geometry, algebraic combinatorics, and representation theory, among others-are used to analyze these two-dimensional wave patterns. The author's primary goal is to explain some details of the classification problem of the soliton solutions of the KP equation (or KP solitons) and their applications to shallow water waves. This book is intended for researchers and graduate students.
(source: Nielsen Book Data)

• Introduction
• What is Quaternionic Spectral Theory?
• Some Historical Remarks on the S-Spectrum
• The Discovery of the S-Spectrum
• Why Did It Take So Long to Understand the S-Spectrum?
• The Fueter-Sce-Qian theorem and spectral theories
• Slice Hyperholomorphic Functions
• Slice Hyperholomorphic Functions
• The Fueter Mapping Theorem in Integral Form
• Vector-Valued Slice Hyperholomorphic Functions
• Comments and Remarks
• The S-Spectrum and the S-Functional Calculus
• The S-Spectrum and the S-Resolvent Operators
• Definition of the S-Functional Calculus
• Comments and Remarks
• The Left Spectrum and the Left Resolvent Operator
• Power Series Expansions and the S-Resolvent Equation
• Properties of the S-Functional Calculus for Bounded Operators
• Algebraic Properties and Riesz Projectors
• The Spectral Mapping Theorem and the Composition Rule
• Convergence in the S-Resolvent Sense
• The Taylor Formula for the S-Functional Calculus
• Bounded Operators with Commuting Components
• Perturbations of the SC-Resolvent Operators
• Some Examples
• Comments and Remarks
• The S-Functional Calculus for n-Tuples of Operators
• The W-Functional Calculus for Quaternionic Operators
• The S-Functional Calculus for Unbounded Operators
• The S-Spectrum and the S-Resolvent Operators
• Definition of the S-Functional Calculus
• Comments and Remarks
• The H-Functional Calculus
• The Rational Functional Calculus
• The S-Functional Calculus for Operators of Type
• The H-Functional Calculus
• Boundedness of the H-Functional Calculus
• Comments and Remarks
• Comments on Fractional Diffusion Processes
• The F-Functional Calculus for Bounded Operators
• The F-Resolvent Operators and the F-Functional Calculus
• Bounded Perturbations of the F-Resolvent
• The F-Resolvent Equations
• The Riesz Projectors for the F-Functional Calculus
• The Cauchy-Fueter Functional Calculus
• Comments and Remarks
• The F-Functional Calculus for n-Tuples of Operators
• The Inverse Fueter-Sce Mapping Theorem
• The F-Functional Calculus for Unbounded Operators
• Relations Between F-Resolvent Operators
• The F-Functional Calculus for Unbounded Operators
• Comments and Remarks
• F-Functional Calculus for n-Tuples of Unbounded Operators
• Quaternionic Operators on a Hilbert Space
• Preliminary Results
• The S-Spectrum of Some Classes of Operators
• The Splitting of a Normal Operator and Consequences
• The Continuous Functional Calculus
• Comments and Remarks
• Spectral Integrals
• Spectral Integrals for Bounded Measurable Functions
• Spectral Integrals for Unbounded Measurable Functions
• Comments and remarks
• The Spectral Theorem for Bounded Normal Operators
• Construction of the Spectral Measure
• The Spectral Theorem and Some Consequences
• Comments and Remarks
• The Spectral Theorem for Unbounded Normal Operators
• Some Transformations of Operators
• The Spectral Theorem for Unbounded Normal Operators
• Some Consequences of the Spectral Theorem
• Comments and Remarks
• Spectral Theorem for Unitary Operators
• Herglotzʼs Theorem in the Quaternionic Setting
• Preliminaries for the Spectral Resolution
• Further Properties of Quaternionic Riesz Projectors
• The Spectral Resolution
• Comments and Remarks
• Spectral Integration in the Quaternionic Setting
• Spectral Integrals of Real-Valued Slice Functions
• Imaginary Operators
• Spectral Systems and Spectral Integrals of Intrinsic Slice Functions
• On the Different Approaches to Spectral Integration
• Bounded Quaternionic Spectral Operators
• The Spectral Decomposition of a Spectral Operator
• Canonical Reduction and Intrinsic S-Functional Calculus for Quaternionic Spectral Operators
• Contents of the Monograph : Quaternionic Closed Operators, Fractional Powers and Fractional Diffusion Processes
• Index
• Bibliography.

The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum. With the purpose of giving a systematic and self-contained treatment of this theory that has been developed in the last decade, the book features topics like the S-functional calculus, the F-functional calculus, the quaternionic spectral theorem, spectral integration and spectral operators in the quaternionic setting. These topics are based on the notion of S-spectrum of a quaternionic linear operator. Further developments of this theory lead to applications in fractional diffusion and evolution problems that will be covered in a separate monograph.
(source: Nielsen Book Data)

• Preface Acknowledgments Author biography
• 1. Models of Nature
• 2. Randomness
• 3. Bayesian and frequentist approaches to scientific inference
• 4. The principles of inferential statistics
• 5. Parametric inference
• 6. Prior distributions and equiprobable events in the physical sciences
• 7. Conclusionsthe statistical nature of scientific knowledge Appendix AShort review of some basic concepts Appendix BAbbreviations.
• (source: Nielsen Book Data)

Science often deals with hard-to-see phenomena, and they only stand out and become real when viewed through the lens of complex statistical tools. This book is not a textbook about statistics applied to science - there are already many excellent books to choose from - rather, it tries to give an overview of the basic principles that physical scientists use to analyze their data and bring out the order of Nature from the fog of background noise.
(source: Nielsen Book Data)