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Exactly Solvable Models

  • D. Ya. Petrina
Chapter
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Part of the Mathematical Physics Studies book series (MPST, volume 17)

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.

Keywords

Thermodynamic Limit Difference Variable Selfadjoint Operator Bose Condensation Canonical Commutation Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • D. Ya. Petrina
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKievUkraine

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