Ergodic property of Markovian semigroups on standard forms of von Neumann algebras

Details Ergodic property of Markovian semigroups on standard forms of von Neumann algebras Ergodic property of Markovian semigroups on standard forms of von Neumann algebras

2005-03-17

arxiv.org/abs/math-ph/0503044v1

Physics

Mathematical Physics

25 pages

Scientific paper

10.1063/1.2113067

We give sufficient conditions for ergodicity of the Markovian semigroups associated to Dirichlet forms on standard forms of von Neumann algebras constructed by the method proposed in Refs. [Par1,Par2]. We apply our result to show that the diffusion type Markovian semigroups for quantum spin systems are ergodic in the region of high temperatures where the uniqueness of the KMS-state holds.

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