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Exactly Solvable Models

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Mathematical Foundations of Quantum Statistical Mechanics

Part of the book series: Mathematical Physics Studies ((MPST,volume 17))

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Abstract

In this section we describe four models of quantum statistical mechanics, namely, the BCS (Bardeen -Cooper-Schrieffer) model of superconductivity, the Bogolyubov model of superfluidity, the model of Huang, Yang, and Luttinger, and the Peierls-Frohlich model. We employ the following scheme: First, we define model Hamiltonians for systems of particles contained in a bounded region (cube) ∧ with periodic boundary conditions and then pass to the thermodynamic limit and study the corresponding limiting model Hamiltonian. The procedure of limit transition is not justified; it enables one to determine the model Hamiltonian of an infinite system which is then studied rigorously.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev, Ukraine

    D. Ya. Petrina

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  1. D. Ya. Petrina
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© 1995 Springer Science+Business Media Dordrecht

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Petrina, D.Y. (1995). Exactly Solvable Models. In: Mathematical Foundations of Quantum Statistical Mechanics. Mathematical Physics Studies, vol 17. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0185-1_6

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  • DOI: https://doi.org/10.1007/978-94-011-0185-1_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4083-9

  • Online ISBN: 978-94-011-0185-1

  • eBook Packages: Springer Book Archive

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