Quantum Markovian semigroups on quantum spin systems: Glauber dynamics

Veni Choi, Chul Ki Ko, Yong Moon Park

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1 Citation (Scopus)

Abstract

We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system (A, τ, ω), where A is a quasi-local algebra, τ is a strongly continuous one parameter group of *-automorphisms of A and ω is a Gibbs state on A. The semigroups can be considered as the extension of semigroups on the nontrivial abelian subalgebra. Let H be a Hubert space corresponding to the GNS representation constructed from ω. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup {Tt}t≥0 on H.The semigroup {Tt}t≥0 acts separately on two subspaces Hd and H0d of H where Hd is the diagonal subspace and H od is the off-diagonal subspace, H= Hd ⊕ H od. The restriction of the semigroup {Tt}t≥0 on H d is Glauber dynamics, and for any η € H0d, Ttη decays to zero exponentially fast as t approaches to the infinity.

Original languageEnglish
Pages (from-to)1075-1087
Number of pages13
JournalJournal of the Korean Mathematical Society
Volume45
Issue number4
DOIs
Publication statusPublished - 2008 Jul

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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