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OverviewThe 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. Full Product DetailsAuthor: J.-B. Bru , W. de Siqueira PedraPublisher: American Mathematical Society Imprint: American Mathematical Society Volume: 224, 1052 Weight: 0.258kg ISBN: 9780821889763ISBN 10: 0821889761 Pages: 155 Publication Date: 30 August 2013 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsPart 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 IndexReviewsAuthor InformationJ.-B. Bru, Universidad del Pais Vasco, Bilbao, Spain. W. de Siqueira Pedra, Universitat Mainz, Germany Tab Content 6Author Website:Countries AvailableAll regions |
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