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Online 1. Angular momentum conservation law in lightfront quantum field theory and extended conformal symmetry of Abelian gauge theory in D ≠ 4 [2018]
 Chiu, YuJu, author.
 [Stanford, California] : [Stanford University], 2018.
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This thesis investigates two independent aspects of spacetime symmetries. The first part of my thesis is about the angular momentum conservation law in lightfront quantum field theory. We prove the lightfront Poincare invariance of the angular momentum conservation law and the helicity sum rule for relativistic composite systems. We show that the lightfront wavefunction (LFWF), which describes the internal structure of a bound state, is in fact frame independent, in contrast to instant form wavefunctions. In particular, we demonstrate that j3, the intrinsic angular momentum projected onto the lightfront direction, is independent of the bound state's 4momentum and the observer's Lorentz frame. The frame independence of j3 is a feature unique to the front form. The angular momentum conservation law leads directly to a nonperturbative proof of the constraint A(0)=1 and the vanishing of the anomalous gravitomagetic moment B(0)=0. Based on the conservation of angular momentum, we derive a selection rule for orbital angular momentum which can be used to eliminate certain interaction vertices in QED and QCD. We also generalize the selection rule to any renormalizable theory and show that there exists an upper bound on the change of orbital angular momentum in scattering processes at any fixed order in perturbation theory. The second part of my thesis investigates an extended conformal symmetry for Abelian gauge theory in general dimensions. Maxwell theory in d \neq 4 spacetime dimensions is an example of a scaleinvariant theory which does not possess conformal symmetry  the special conformal transformation (SCT) explicitly breaks the gauge invariance of the theory. We construct a nonlocal gaugeinvariant extension of the SCT, which is compatible with the BRST formalism and defines a new symmetry of the physical Hilbert space of the Maxwell theory for any dimension d \geqslant 3. We prove the invariance of Maxwell theory in d \geqslant 3 by explicitly showing that the gaugeinvariant twopoint correlation functions, the action, and the classical equation of motion are unchanged under such a transformation.
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3781 2018 C  Unavailable In process 
 Benjamin, Nathan, author.
 [Stanford, California] : [Stanford University], 2018.
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In this thesis, we study aspects of threedimensional gravity in Anti de Sitter (AdS) space by studying the holographically dual twodimensional conformal field theory (CFT). We begin by describing general constraints on the elliptic genus of a twodimensional supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature, using symmetric orbifolds as a case study. We then move on to study extremal theories, conjectured to be dual to "pure" threedimensional gravity. We first provide an example of an extremal chiral N=2 superconformal field theory at c=24. We then consider extremal CFTs at large central charge, and consider the quantum corrections to the classical spectrum. Our conjecture passes various consistency checks, especially when generalized to include theories with supersymmetry. Finally, we examine a specific topdown construction of AdS3/CFT2 from string theory, called the D1/D5 system. We examine the lowlying quarter BPS spectrum of the K3 symmetric orbifold CFT at various points in moduli space, and look at a more refined count than the ordinary elliptic genus. We do a decomposition of the spectra into N=4 characters, and show that at large N the character decomposition satisfies an unusual property, in which the degeneracy only depends on a certain linear combination of left and rightmoving quantum numbers, suggesting deeper symmetry structure.
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Online 3. Complexity and black hole geometry [2018]
 Zhao, Ying, author.
 [Stanford, California] : [Stanford University], 2018.
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This thesis discusses various aspects of black hole interior. We explore the connection between black hole geometry and quantum complexity. We look for quantum circuit protocols corresponding to traversable wormhole. We also point out various puzzles we encountered.
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Online 4. Exploring dark matter with improved numerical techniques [2018]
 Powell, Devon, author.
 [Stanford, California] : [Stanford University], 2018.
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In this thesis, I discuss several computational physics developments. The context is the study of potential dark matter observables calculated from traditional cosmological Nbody simulations. These particlebased simulation techniques often suffer from shot noise when sampling of the density field. Building on the phase space sheet (PSS) interpretation of Abel, Hahn and Kaehler (2012) of cold collisionless fluid, I develop a method for geometrically exact and robust volume and pointsampling algorithms. These operate on a simplicial tessellation of a 3manifold embedded in the 6D phase space, such that the mass is interpolated between particles, which are interpreted as Langrangian flow tracers. This results in a smooth continuous and noise free density field that aids accurate interpretations of cosmological dark matter simulations. I discuss the application of these algorithmic developments to the indirect detection of dark matter (via decay and annihilation), studies of cosmic voids, the cosmic neutrino background, and simulations. I also present recent work on extending these concepts to radiation transport with "adaptive beam tracing." This method extends raytracing, which follows 1dimensional rays along their trajectories, to beam tracing, which instead volumesamples 3D photon packets called "beams".
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Online 5. Improved discrimination for neutrinoless double beta decay searches with EXO200 and nEXO [electronic resource] [2018]
 Fudenberg, Daniel.
 2018.
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Neutrinos have been shown to have nonzero mass, however how they generate their minuscule masses is an open question. One well motivated possibility is that neutrinos have Majorana masses, for which the most sensitive test is the observation of neutrinoless doublebeta decay. The halflife of this neutrinoless mode is much slower than that of the observed twoneutrino mode of doublebeta decay, which is many orders longer than the age of the universe, thus searches are heavily background dominated. In this work discusses two, completely distinct, methods to improve discrimination of neutrinoless doublebeta decay, of xenon136, from backgrounds. The first method is through training new discriminators to more fully exploit the observed topological information in EXO200 to distinguish neutrinoless doublebeta decay from the most common backgrounds. The second method is to enable the observation of barium136 resulting from doublebeta decay for a future generation detector via a hardwarecentric approach. One path requires extraction from high pressure gas to vacuum of heavy ions from similarly heavy medium with high efficiency. Work on a prototype extraction apparatus for the nEXO collaboration and lessons learned are presented here.
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3781 2018 F  Inlibrary use 
 Kurinsky, Noah, author.
 [Stanford, California] : [Stanford University], 2018.
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The SuperCDMS SNOLAB experiment will be a 20kg scale Si and Ge direct dark matter detection experiment designed to probe down to 300 MeV in dark matter (DM) mass through DMnucleus scattering and 500 keV in DM electron scattering. In order to reach these low masses with appreciable sensitivity to dark matter, it needs to achieve very low energy resolution (≤ 10 ev) for nuclear recoils in both detector materials, which will be achieved using a new detector design and operating mode, CDMS HV. This detector is designed to operate at a bias of 100V to convert charges liberated in our detector targets to into phonon energy in order to resolve individual electronhole pairs. This has never before been achieved in a kgscale detector. In this thesis, I cover three elements of the design of the CDMS HV detectors. I discuss the detector physics controlling how charges and phonons are generated in our detector crystals, com paring theory to results of recent experiments carried out at Stanford. I move on to describe the operating principles of our phononmediated charge readout, as well as the design of the CDMS HV detector. I then describe the performance tests of early CDMS HV prototypes in conjunction with the SuperCDMS SNOLAB electronics, and discuss the path towards achieving single electronhole pair resolving detectors at the kgscale given the performance obtained thus far. As a result of these tests, we were able to refine our noise and sensor dynamics models, and develop new metrics for diagnosing nonideal sources of noise to aid in reducing coupling of the external environment to our detectors. In order to study the microphysics of phonon and charge production in our target crystals, we fabricated a number of gramscale devices with various sensor designs in order to separate sensor and environmental effects from intrinsic crystal properties. These devices provided the first successful demonstrating of using voltage to amplify charge energy by production of phonons (the NeganovTrofimovLuke effect) in order to resolve electronhole pairs, and opened up a new regime of dark matter and photon science at the gramscale that we are just beginning to explore. A first dark matter search was carried out with one of these gramscale devices, producing worldleading limits on electronrecoiling dark matter between 0.5 and 5 MeV in dark matter mass for multiple form factors. This device achieved a phonon resolution of 10 eV, allowing a single gramday of exposure to rival kgdays of exposure in the competing liquidnoble based electronrecoil search.
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Online 7. Quantum error correction and spacetime [2018]
 Salton, Grant, author.
 [Stanford, California] : [Stanford University], 2018.
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Quantum error correction (QEC) is a branch of quantum information theory, originally invented to protect hypothetical quantum computers against realistic sources of noise. QEC has enjoyed significant success within the paradigm of computation, but the ideas and techniques of quantum error correction have also been effective in tools many fields of physics. In this thesis, we will shed light on the way in which QEC manifests outside of the usual computational paradigm and informs other areas of physics. We'll focus on the role of QEC in quantum gravity, spacetime, and high energy theoretical physics. We start with the general problem of quantum information replication in spacetime, and we show that information replication is possible if and only if transmission of the quantum information does not result in cloning of quantum information or fasterthanlight communication. We then study the role of quantum error correction in quantum gravity, specifically within a gaugegravity duality known as AdS/CFT. We establish a new formula for mapping observables on either side of the duality, showing that the socalled bulktoboundary map defines an approximate quantum error correcting code. Motivated by the study of entangled states dual to multiboundary wormholes in AdS/CFT, we then turn our attention to characterizing the states that can arise from the euclidean path integral in threedimensional ChernSimons theories. We study U(1) level k and SO(3) level k ChernSimons theories on euclidean 3manifolds with torus boundaries. For the abelian U(1) theory, we find that the set of states that can be prepared exactly coincides with the set of stabilizer states, which are characterized by quantum error correcting codes. For the nonabelian SO(3) theory, we find that any state can be prepared to arbitrary precision, giving rise to a notion of state universality. We conclude with some final observations to support the idea that entanglement gives rise to the connectedness of spacetime. We study the partial transpose of the thermofield double (TFD) state geometrically, and we demonstrate that local time reversal (which is unitarily equivalent to partial transpose) leads to inconsistencies in the connected spacetime dual to the TFD state.
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Online 8. Searching materials for novel physics from theory and from data [electronic resource] [2018]
 Zhou, Quan.
 2018.
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Materials search and discovery is crucially important in condensed matter physics. Besides experimental trialanderrors, there exist two types of methods to guide materials explorations: "from theory" that starts from theoretic analysis and numerical simulations, and "from data" that leverages massive materials data via statistical machine learning. I will present one work for each of both methods of materials discovery in this dissertation. Firstly, I will discuss the theoretic proposal and materials realization of antiferromagnetic Dirac semimetal. I will specifically show how a nonsymmorphic crystal symmetry stabilizes a fourfold degenerate point in the electronic band structure of an antiferromagnetic system that is invariant under the combination of timereversal and inversion symmetry, thus realizing massless Dirac fermions as low energy excitations. Secondly, I will talk about how to learn atoms' properties from extensive materials data, inspired by ideas from computational linguistics. I will present analysis of the constructed atom vectors, as well as their applications in databased materials prediction using machine learning.
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Online 9. Stringy nonlocality and black hole physics [2018]
 Dodelson, Matthew, author.
 [Stanford, California] : [Stanford University], 2018.
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We analyze nonlocal effects in string theory near black hole horizons. Due to extended string effects, early infalling matter can be detected by late observers long after they fall into the black hole. The nonlocal effects are derived via an analysis of the sixpoint string scattering matrix in flat space, as well as by probing the scattering with a background dilaton. We also derive simple new string solutions in three dimensions.
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Online 10. Thermalization near integrability in a dipolar quantum Newton's cradle [electronic resource] [2018]
 Tang, Yijun.
 2018.
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Ultracold atomic gases are powerful platforms for studying isolated, nearly ideal quantum systems. Recent advancements in laser cooling and trapping of magnetic lanthanide atoms have introduced magnetic dipoledipole interaction into the toolbox of ultracold atomic physics. When coupled with the shortranged Van der Waals interaction, the longranged and anisotropic dipolar interaction dramatically modifies the atomic gas properties. This thesis presents experimental studies of ultracold gases of dysprosium (Dy)  the most magnetic atom. We measured the strength of the Van der Waals interaction in bosonic gases of Dy. Furthermore, we studied how the interplay between the Van der Waals and the dipolar interactions affects expansion dynamics in thermal Dy gases. We have also characterized the anisotropic atomic polarizability near the Dy 741nm narrowline transition. These measurements led to the creation of the first dipolar quantum Newton's cradle, with which we studied thermalization in a nearly integrable onedimensional gas with a tunable integrability breaking dipolar interaction.
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Online 11. Thin silicon and metalassisted chemical etching for photovoltaic and electronic devices [2018]
 Lai, Ruby A., author.
 [Stanford, California] : [Stanford University], 2018.
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Ultrathin silicon membranes, less than 20um thick, have extreme flexibility, lightness, and the superior materials quality and advantages in silicon microprocessing. There are two major roadblocks in developing ultrathin silicon membranes: the fabrication processing of the more delicate material in traditional CMOS fabrication, and the manufacturing of high quality, ultrathin sheets from bulk Si material. First, I use alkaline silicon etching of silicon wafers to form ultrathin silicon sheets, supported by a thick ring of Si material on its edge, that enable facile processing of large 3" sheets in traditional CMOS apparatuses. Second, I explored the novel use of a "chemical wafersaw" for silicon by using metalassisted chemical etching, as a possible pathway to create thin silicon sheets. Third, I developed a new theoretical model for the mechanism of metalassisted chemical etching of silicon, which explained for the first time the silicon doping dependence of the etch. Fourth, I present computational design and fabrication of a novel nanophotonic solar cell contact for a metalinsulatorsemiconductor solar cell, as well as other nanostructures, fabricated using metalassisted chemical etching.
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Online 12. Aspects of cosmology and black hole physics in string theory [electronic resource] [2017]
 Wenren, Danjie.
 2017.
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Over the past few decades string theory has provided us with many novel ideas and models of physics where the interplay of gravity and quantum mechanics is crucial. In particular it has been widely used in the study of black hole physics and cosmology. This thesis describes three aspects of string theory's application in these two fields. First we consider open string pair production effects near hyperbolic black holes in Antide Sitter space (AdS). It is shown that these black holes can decay by radiating Dbranes and there can be nonadiabatic pair production of open strings stretched between those radiated branes. In the second part we switch to cosmology, where we consider two models inspired by axion monodromy, which is very natural in string theory. First we study heavy fermion production effects, which come from the assumption that the fermion mass is modulated by the inflaton field, and its signature on primordial Nspectra. A detailed comparison between this effect and the effect of boson production is made. Lastly, we consider the case where there are a large number of axions that collectively drive inflation. It is shown that the spectral index and the tensortoscalar ratio depend on the distribution of parameters of the axion fields. This thesis is based on papers [1, 2, 3].
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Online 13. Atomistic modeling of highpressure silica crystallization under dynamic compression [electronic resource] [2017]
 Shen, Yuan.
 2017.
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Understanding the kinetics of shockcompressed SiO2 is of great importance for mitigating optical damage for highintensity lasers and for understanding meteoroid impacts. Experimental work has placed some thermodynamic bounds on the formation of highpressure phases of this material, but the formation kinetics and underlying microscopic mechanisms are yet to be elucidated. In this study, by employing multiscale molecular dynamics studies of shockcompressed fused silica and quartz, we find that silica transforms into a poor glass former that subsequently exhibits ultrafast crystallization within a few nanoseconds. We also find that, as a result of the formation of such an intermediate disordered phase, the transition between silica polymorphs obeys a homogeneous reconstructive nucleation and grain growth model. We construct a quantitative model of nucleation and grain growth, and compare its predictions with highpressure silica crystal grain sizes observed in laserinduced damage and meteoroid impact events. Moreover, we have studied the quantum nuclear effects for highpressure silica crystallization. While quantum nuclear effects play important roles in shockinduced chemical reactions and phase transitions, they are absent in classical atomistic shock simulations. To address this shortcoming, we couple the shock simulation with a colorednoise Langevin thermostat. We find that this semiclassical approach gives shock temperatures as much as 7% higher than classical simulations near the onset of crystallization in silica. We have also studied the impact of this approach on the kinetics of crystallization and the position of highpressure silica melt line.
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Online 14. Automorphy, geometry, and symmetries of BPS states [electronic resource] [2017]
 Paquette, Natalie M.
 2017.
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A host of new observations regarding BPS states in supersymmetric string compactifications point towards tantalizing new mathematical structures underlying string theory. The mathematical subjects of finite group theory, number theory (especially modular and mock modular forms), vertex operator algebras, generalized KacMoody algebras, enumerative geometry, and more have come to the fore in string theory of late, prompted in part by the ``Mathieu moonshine" observation in 2010 by Eguchi, Ooguri, and Tachikawa. This thesis describes progress in understanding mathematical aspects of string compactifications, with a focus on Mathieu and Umbral moonshines, automorphic forms, manifolds of special holonomy, and the algebraic and symmetric properties enjoyed by BPS subspaces of string theory. We make progress towards using string theory as an explanatory framework that ties together some of these mathematical disciplines. We also employ new mathematical ideas to constrain and describe highly symmetric string vacua.
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3781 2017 P  Inlibrary use 
 Gu, Yingfei.
 2017.
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The butterfly effect, as an icon for the chaotic dynamics, refers to the exponential sensitivity on the initial conditions. This phenomenon is common in daily life, e.g. it explains the difficulty of long time weather reports. For physicists, the idea of the chaotic dynamics helps to understand the ergodicity of a classical complex system and therefore is essential for the statistical mechanics and thermodynamics. In the microscopic manybody systems governed by quantum mechanics, the chaotic dynamics is also expected to be generic and ultimately helpful for the understanding of the quantum thermalization. What I will show in this dissertation is that the quantum butterfly effect could also provide precise information about the nontrivial properties of the manybody interacting systems, such as thermal transport and topological properties. I will employ two classes of solvable models: the SachdevYeKitaev model in high dimensions and the rational conformal field theories in two dimensions to explicitly present the unexpected connection between the butterfly effect and other aspects of the model.
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Online 16. Constructing scattering amplitudes from their formal properties [electronic resource] [2017]
 McLeod, Andrew.
 2017.
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Scattering amplitudes in quantum field theory encode the probability of configurations of incoming and outgoing particles scattering into each other, as well as particle masses and decay rates. Traditionally they have been calculated using Feynman diagrams, but this method generally proves too computationally intensive to allow for the calculation of higherloop contributions, which are relevant for making predictions in particle physics experiments and to our understanding of quantum field theory itself. As a step in the direction of filling this computational gap, this dissertation presents an improved bootstrap method for computing scattering amplitudes in the planar limit of maximally supersymmetric YangMills theory. This method does away with Feynman diagrams altogether, and instead uses knowledge of the symmetries and analytic properties of scattering amplitudes, in conjunction with an understanding of the mathematical form these amplitudes take in general and special kinematics, to uniquely determine them at high loop orders. In particular, it makes use of the fact that amplitudes in this theory are expressible in terms of generalized polylogarithms for seven and fewer particles. The first part of this dissertation focuses on sixparticle kinematics, where previouslyunappreciated algebraic constraints on these amplitudes are described that restrict both their double derivatives and their double discontinuities. Alongside previouslyunderstood constraints, these properties are used to uniquely determine all sixparticle amplitudes in this theory through five loops. These explicit results are then used to provide analytic and numerical evidence for a recentlyconjectured positivity property these amplitudes are thought to have in certain kinematic regions. In the second part of this dissertation, it is shown that these methods straightforwardly generalize to sevenparticle kinematics, where they in fact prove to be even more restrictive than in sixparticle kinematics. In particular, a smaller set of constraints is shown to be sufficient to determine specific sevenpoint amplitudes at three and four loops, up to integration constants. While the results presented in this thesis are confined to the planar limit of maximally supersymmetric YangMills theory, these bootstrap methods are expected to prove useful even in theories without supersymmetry.
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Online 17. Couplings of phonons to light and one another studied with LCLS [electronic resource] [2017]
 Henighan, Thomas.
 2017.
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Engineering the thermal properties of materials plays a crucial role in technologies including propulsion, computing, optics, and household appliances. Lattice vibrations, or phonons, are at the heart of our understanding of heat in solids. It is thus beneficial to continue exploring the basic science of phonons not only for the purpose of expanding human knowledge, but for making possible further advances in materials engineering as they pertain to heat. Fundamental to the theory of phonons is the phonon dispersion, the relationship between phonons' momentum and their energy. Momentum resolved inelastic scattering of neutrons and xrays provides experimental access to this dispersion [1, 2]. An accurate measure of a material's phonon dispersion can allow for accurate prediction of its heat capacity, interatomicbonding strengths, and sound propagation speed amongst other things. However the phonon dispersion gives us no direct information on how phonons couple to other excitations and/or one another, which is important for macroscopic thermal properties. For instance thermal expansion and finite thermal conductivity are consequences of finite phononphonon coupling. Current methods for measuring such interactions are indirect, including measurement of phonon linewidths and measurements of thermal conductivity. Timeresolved measurements can be useful for measuring couplings by observation of energy transfer between excitations with time. Thus a time and momentum resolved measure of phonons would seem an obvious tool for studying their couplings to one another and other excitations. While optical measurements can provide exquisite time resolution, they can resolve only very small momentum shifts. Traditional neutron and xray sources have the necessary momentum resolution, but the pulses are too long (~100 picoseconds or more) to resolve the transfer of energy of picosecond timescales, relevant to phononphonon coupling. Plasmabased xray sources have su cient momentum and time resolution, but the flux is too low to measure weak di↵raction signals from phonons in a reasonable amount of time. The Linac Coherent Light Source (LCLS) is the first instrument to provide all the aspects neces sary for time and momentum resolved measurement of phonon energy transfer, with shortwavelength (~1 angstrom), shorttime (~10s of femtoseconds) pulses at high flux (~10^13 photons/second) [3]. Trigo et al showed that this new tool can be used to measure phonon dispersions in a timeresolved way [4]. Specifically, they showed that a short optical pump can be used to excite temporal coherences for phonons throughout the Brillouin zone that can be observed in the timeresolved xray scattering from a delayed LCLS xray pulse. The work of this thesis was motivated by the desire to use LCLS to make fundamentally new measurements of phonon coupling. To do this we use variations of the technique of Trigo et al. We first explore further the principles behind the technique, specifically the mechanism by which short wavelength light couples to highwavevector phonons. We find that the opticalphonon copuling is of second order in the phonons, exciting correlated pairs of phonons with nearly equal and opposite momentum. Next, we explore a method for measurement of energy transfer in the parametric downconversion of a zonecenter phonon in crystalline bismuth. The result is, to our knowledge, the first time and momentum resolved measurement of phonon decay channels. Finally, we show that a shaped optical pump pulse may be used to achieve frequencyselective excitation of the phonons. Taken together, these results suggest tools like LCLS may be used to make measurements of phononphonon coupling strengths that were previously inaccessible experimentally.
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Online 18. Depth perception in holography [electronic resource] [2017]
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According to the holographic principle, information about our world can be encoded in a projection of one less dimension, similar to a hologram. This principle has culminated in the discovery of the AdS/CFT duality, an explicit example of holography where, miraculously, the lowerdimensional projection is a theory of familiar local fields. But how is the extra dimension encoded in this holographic theory? The equivalence between a gravitational theory and a lowerdimensional theory implies a radical reorganization of the degrees of freedom: the fundamental building blocks of a gravitational theory are likely extended, not pointlike, objects. In this thesis, I describe progress towards formulating both sides of the duality in terms of extended probes  objects which naturally possess the ability of "holographic depth perception.".
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3781 2017 M  Inlibrary use 
 Desmond, Harry.
 2017.
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Dark matter halos comprise the bulk of the universe's mass, yet must be probed by the luminous galaxies that form within them. A key goal of modern astrophysics is to robustly relate the visible and dark mass, which to first order means relating the properties of galaxies and halos. The aim of this thesis is to develop and evaluate models of the galaxyhalo connection using observations of galaxy dynamics. In particular, I build empirical models based on the technique of halo abundance matching for five key dynamical scaling relations of galaxies  the TullyFisher, FaberJackson, masssize and mass discrepancyacceleration relations, and Fundamental Plane  which relate their baryon distributions and rotation or velocity dispersion profiles. I then develop a statistical scheme based on approximate Bayesian computation to compare the predicted and measured values of a number of summary statistics describing the relations' important features. I find some features to be naturally accounted for by an abundance matching approach and others to impose new constraints on the galaxyhalo connection; the remainder are challenging to reproduce and may imply galaxyhalo correlations beyond the scope of basic abundance matching. Besides providing concrete statistical tests of specific galaxy formation theories, these results will be of use for guiding the inputs of empirical and semianalytic galaxy formation models, which require galaxyhalo correlations to be imposed by hand.
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Online 20. A Fermi liquid perspective on the high field ground state of the cuprate superconductors [electronic resource] [2017]
 Maharaj, Akash V.
 2017.
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The nature of the parent metallic state from which high temperature superconductivity emerges has remained fiercely controversial in the three decades since the discovery of the cuprate superconductors. Surprisingly, recent experiments in magnetic fields high enough to quench superconductivity have revealed a metallic state whose properties are remarkably conventional, and well explained within the context of Fermi liquid theory. Yet, even within this paradigm, these experiments have raised several fundamental theoretical questions. This thesis focuses on a few such experimentally motivated matters of theoretical principle. The primary themes involve issues surrounding quantum oscillations, as well as the recent discovery of charge density waves (CDWs) in the underdoped cuprates. I begin with a discussion of how charge density waves in YBCO can be related to earlier discovered stripes in the `214' family of cuprates, and also consider the experimental consequences of the resulting vestigial orders which break discrete rotational and/or mirror symmetries. I show that Xray scattering measurements of seemingly biaxial CDW order, can in fact originate from a three dimensional `crisscrossed' pattern of stripes. This three dimensional pattern breaks mirror symmetries, leading to sharp consequences for quantum oscillation spectra, possible detection in elastoresistance experiments, and each of these topics form chapters of this thesis. The discussion of quantum oscillations starts by considering whether they are even possible in the presence of incommensurate CDWs that formally destroy translation symmetry, rendering the concept of a Fermi surface approximate at best. Using exact dualities, I show that quantum oscillations are no longer periodic in 1/B, and even disappear for sufficiently strong incommensurate CDWs. In a subsequent chapter, I use similar dualities to constrain the form of the Fermi surface that is possible in YBCO, and discuss the strong evidence for both mirror symmetry breaking and significant quasiparticle renormalization. Finally, I examine the behavior of the Hall number of a metal when nematicity results in a Lifshitz transition where the Fermi surface topology evolves from a closed pocket to open sheets. I provide analytic expressions for the critical behavior of the Hall number, and also relate these results to recent experiments in the cuprates. I conclude this thesis by synthesizing these ideas into a proposed doping evolution for the Fermi surface of an idealized cuprate.
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