Noncooperative equilibria of Fermi systems with long range interactions
 Author/Creator
 Bru, J.B. (JeanBernard), 1973
 Language
 English.
 Publication
 Providence, Rhode Island : American Mathematical Society, 2013.
 Physical description
 xi, 155 pages ; 26 cm.
 Series
 Memoirs of the American Mathematical Society ; no. 1052.
Access
Available online

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QA3 .A57 NO.1052

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QA3 .A57 NO.1052
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Contributors
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Part 1. Main Results and Discussions: Fermi systems on lattices Fermi systems with longrange interactions Part 2. Complementary Results: Periodic boundary conditions and Gibbs equilibrium states The set $E_{\vec{\ell}}$ of $\vec{\ell}.\mathbb{Z}^{d}$invariant states Permutation invariant Fermi systems Analysis of the pressure via t.i. states Purely attractive longrange Fermi systems The maxmin and minmax variational problems Bogoliubov approximation and effective theories Appendix Bibliography Index of notation Index.
 (source: Nielsen Book Data)
 Publisher's Summary
 The authors define a Banach space $\mathcal{M}_{1}$ of models for fermions or quantum spins in the lattice with long range interactions and make explicit the structure of (generalised) equilibrium states for any $\mathfrak{m}\in \mathcal{M}_{1}$. In particular, the authors give a first answer to an old open problem in mathematical physicsfirst addressed by Ginibre in 1968 within a different context  about the validity of the socalled Bogoliubov approximation on the level of states. Depending on the model $\mathfrak{m}\in \mathcal{M}_{1}$, the authors' method provides a systematic way to study all its correlation functions at equilibrium and can thus be used to analyse the physics of long range interactions. Furthermore, the authors show that the thermodynamics of long range models $\mathfrak{m}\in \mathcal{M}_{1}$ is governed by the noncooperative equilibria of a zerosum game, called here thermodynamic game.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Responsibility
 J.B. Bru, W. de Siqueira Pedra.
 Series
 Memoirs of the American Mathematical Society, 00659266 ; no. 1052
 Note
 "July 2013, Volume 224, Number 1052 (first of 4 numbers)."
 ISBN
 9780821889763
 0821889761