Titlebook: C*-Algebras and Mathematical Foundations of Quantum Statistical Mechanics; An Introduction Jean-Bernard Bru,Walter Alberto de Siqueira Pedr

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Micha? Kalecki: An Intellectual Biographys. Here, we extend this approach to quantum lattice models including additional mean-field interaction terms, which can be seen as an extreme form of . interactions. We show how the variational principle for equilibrium states of the previous chapter can be extended to include mean-field models (lik

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C*-Algebras and Mathematical Foundations of Quantum Statistical MechanicsAn Introduction

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Micha? Kalecki: An Intellectual Biographyel presents a first-order phase transition) at low temperatures. Note that realistic effective interparticle interactions of quantum many-body systems are widely seen as being short-range, but they are extremely difficult to analyze, in general, with many important fundamental questions remaining op

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Thermodynamic Equilibrium of Finite Quantum Systems, to understand the relation between these mathematical properties, starting from the finite dimension case. Later on, in Chaps. . and ., we will use the static properties of Gibbs states to define and study the thermodynamic equilibrium of infinite quantum system.

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Elements of ,-Algebra Theory, more transparent the essential differences between the classical and quantum realms, as well as their common features. We also study various important properties of the positive normalized linear functionals on these algebras (i.e., their states). In the last part of this chapter, we present the so