Topics in quantum statistical mechanics and operator algebras

2001/07/11 by David Ruelle, Ruelle, David
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #FOS: Physical sciences #Mathematical Physics (math-ph) #Random Matrices and Applications #Spectral Theory in Mathematical Physics #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0107009

Lecture notes, 36 pages

arxiv created 2001/07/11 · openalex publication_date 2001/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications in mind. In Chapter 2 we study some questions related to the quantum statistical mechanics of spin systems, with particular attention to the time evolution of infinite systems. The basic reference for these two chapters is Bratteli-Robinson: Operator algebras and quantum statistical mechanics I, II. In Chapter 3 we discuss the nonequilibrium statistical mechanics of quantum spin systems, as it is currently being developped.

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