Ergodic property of Markovian semigroups on standard forms of von Neumann algebras
arXiv:math-ph/0503044 · doi:10.1063/1.2113067
Abstract
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.
arXiv comment25 pages