Non-cooperative equilibria of Fermi systems with long range interactions
著者
書誌事項
Non-cooperative equilibria of Fermi systems with long range interactions
（Memoirs of the American Mathematical Society, no. 1052）
American Mathematical Society, c2012
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注記
"July 2013, volume 224, number 1052 (first of 4 numbers)."
Includes bibliographical references (p. 143-145) and indexes
内容説明・目次
内容説明
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 physics--first addressed by Ginibre in 1968 within a different context - about the validity of the so-called 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 non-cooperative equilibria of a zero-sum game, called here thermodynamic game.
目次
Part 1. Main Results and Discussions:
Fermi systems on lattices Fermi systems with long-range 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 long-range Fermi systems
The max-min and min-max variational problems
Bogoliubov approximation and effective theories
Appendix
Bibliography
Index of notation Index
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