Quantum Markovian semigroups on quantum spin systems: Glauber dynamics
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We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system (A, γ, ω), where A is a quasi-local algebra, γ 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 Hilbert 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 Hod of H, where Hd is the diagonal subspace and Hod is the off-diagonal subspace, H = Hd Hod. The restriction of the semigroup {Tt}t≥0 on Hd is Glauber dynamics, and for any η∈ Hod, Ttη decays to zero exponentially fast as t approaches to the infinity.
Abstract
We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system (A, γ, ω), where A is a quasi-local algebra, γ 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 Hilbert 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 Hod of H, where Hd is the diagonal subspace and Hod is the off-diagonal subspace, H = Hd Hod. The restriction of the semigroup {Tt}t≥0 on Hd is Glauber dynamics, and for any η∈ Hod, Ttη decays to zero exponentially fast as t approaches to the infinity.
참고문헌 (9)
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