Topics in quantum statistical mechanics and operator algebras

Details Topics in quantum statistical mechanics and operator algebras Topics in quantum statistical mechanics and operator algebras

2001-07-11

arxiv.org/abs/math-ph/0107009v1

Physics

Mathematical Physics

Lecture notes, 36 pages

Scientific paper

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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