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

Yong Moon Park
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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.

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Yong Moon Park. 2005-03-17. Ergodic property of Markovian semigroups on standard forms of von Neumann algebras. https://doi.org/10.1063/1.2113067

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