David Ruelle
Topics in quantum statistical mechanics and operator algebras
(84K, plain tex)
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. These are
notes corresponding to lectures given at Rutgers, Math. Dept.
in 1999-2000.