Uniqueness regime for Markov dynamics on quantum lattice spin systems

Abstract

We consider a lattice of weakly interacting quantum Markov processes. Without interaction, the dynamics at each site is relaxing exponentially to a unique stationary state. With interaction, we show that there remains a unique stationary state in the thermodynamic limit, i.e. absence of phase coexistence, and the relaxation towards it is exponentially fast for local observables. We do not assume that the quantum Markov process is reversible (detailed balance) w.r.t. a local Hamiltonian.

v1 -> v2: improved presentation, matches published version

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• Heat Conduction and Entropy Production in Anharmonic Crystals with Self-Consistent Stochastic Reservoirs
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Cited by in corpus (6)

• Relaxation times of dissipative many-body quantum systems
• Dissipative Bose-Einstein condensation in contact with a thermal reservoir
• An exponentially local spectral flow for possibly non-self-adjoint perturbations of non-interacting quantum spins, inspired by KAM theory
• Perturbative criteria for the ergodicity of interacting dissipative quantum lattice systems
• Perturbation bounds of Markov semigroups on abstract states spaces
• Stability of the uniqueness regime for ferromagnetic Glauber dynamics under non-equilibrium perturbations