QUANTUM MARKOVIAN SEMIGROUPS ON QUANTUM SPIN SYSTEMS: GLAUBER DYNAMICS

Title & Authors
QUANTUM MARKOVIAN SEMIGROUPS ON QUANTUM SPIN SYSTEMS: GLAUBER DYNAMICS
Choi, Veni; Ko, Chul-Ki; Park, Yong-Moon;

Abstract
We study a class of KMS-symmetric quantum Markovian semigroups on a quantum spin system ($\small{\mathcal{A},{\tau},{\omega}}$), where $\small{\mathcal{A}}$ is a quasi-local algebra, $\small{\tau}$ is a strongly continuous one parameter group of *-automorphisms of $\small{\mathcal{A}}$ and $\small{\omega}$ is a Gibbs state on $\small{\mathcal{A}}$. The semigroups can be considered as the extension of semi groups on the nontrivial abelian subalgebra. Let $\small{\mathcal{H}}$ be a Hilbert space corresponding to the GNS representation con structed from $\small{\omega}$. Using the general construction method of Dirichlet form developed in [8], we construct the symmetric Markovian semigroup $\small{\{T_t\}{_t_\geq_0}}$ on $\small{\mathcal{H}}$. The semigroup $\small{\{T_t\}{_t_\geq_0}}$ acts separately on two subspaces $\small{\mathcal{H}_d}$ and $\small{\mathcal{H}_{od}}$ of $\small{\mathcal{H}}$, where $\small{\mathcal{H}_d}$ is the diagonal subspace and $\small{\mathcal{H}_{od}}$ is the off-diagonal subspace, $\mathcal{H} Keywords KMS symmetric quantum Markovian semigroups;quantum spin systems;diagonal subspace;Glauber dynamics; Language English Cited by 1. Linear and Nonlinear Dissipative Dynamics, Reports on Mathematical Physics, 2016, 77, 3, 377 References 1. L. Accardi and S. Koyzyrev, Lectures on quantum interacting particle systems, Quantum interacting particle systems (Trento, 2000), 1-195, QP-PQ: Quantum Probab. White Noise Anal., 14, World Sci. Publ., River Edge, NJ, 2002 2. S. Albeverio and R. Hoegh-Krohn, Dirichlet forms and Markovian semigroups on$C^{\ast}\$-algebras, Comm. Math. Phys. 56 (1997), 173-187

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