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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.
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참고문헌 (9)
참고문헌 신청
C. Bahn / 2003 / Dirichlet forms and symmetric Markovian semigroups on CCR algebras with respect to quasi-free states / Journal of Mathematical Physics 44 (2) : 723 ~ 753
D. Goderis / 1991 / Constructing quantum dissipations and their reversible states from classical interacting spin systems / Annales de l'Institut Henri Poincare. Physique The
F. Cipriani / 1997 / Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras / Journal of Functional Analysis 147 (2) : 259 ~ 300
K. R. Parthasarathy / 1992 / An Introduction to Quantum Stochastic Calculus / Birkhauser Verlag
L. Accardi / 2002 / Lectures on quantum interacting particle systems, Quantum interacting particle systems (Trento, 2000) / QP?PQ: QUANTUM PROBABILITY AND WHITE NOISE ANALYSI
D. Goderis / 1991 / Constructing quantum dissipations and their reversible states from classical interacting spin systems / Annales de l'Institut Henri Poincare. Physique The
F. Cipriani / 1997 / Dirichlet forms and Markovian semigroups on standard forms of von Neumann algebras / Journal of Functional Analysis 147 (2) : 259 ~ 300
K. R. Parthasarathy / 1992 / An Introduction to Quantum Stochastic Calculus / Birkhauser Verlag
L. Accardi / 2002 / Lectures on quantum interacting particle systems, Quantum interacting particle systems (Trento, 2000) / QP?PQ: QUANTUM PROBABILITY AND WHITE NOISE ANALYSI
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