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

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 by Park. 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.

Authors:
 [1]
  1. Department of Mathematics, Yonsei University, Seoul 120-749 (Korea, Republic of)
Publication Date:
OSTI Identifier:
20699623
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 46; Journal Issue: 11; Other Information: DOI: 10.1063/1.2113067; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; DIFFUSION; GROUP THEORY; MARKOV PROCESS; SPIN

Citation Formats

Park, Yong Moon. Ergodic property of Markovian semigroups on standard forms of von Neumann algebras. United States: N. p., 2005. Web. doi:10.1063/1.2113067.
Park, Yong Moon. Ergodic property of Markovian semigroups on standard forms of von Neumann algebras. United States. doi:10.1063/1.2113067.
Park, Yong Moon. Tue . "Ergodic property of Markovian semigroups on standard forms of von Neumann algebras". United States. doi:10.1063/1.2113067.
@article{osti_20699623,
title = {Ergodic property of Markovian semigroups on standard forms of von Neumann algebras},
author = {Park, Yong Moon},
abstractNote = {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 by Park. 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.},
doi = {10.1063/1.2113067},
journal = {Journal of Mathematical Physics},
number = 11,
volume = 46,
place = {United States},
year = {Tue Nov 01 00:00:00 EST 2005},
month = {Tue Nov 01 00:00:00 EST 2005}
}