Uniqueness regime for Markov dynamics on quantum lattice spin systems

@article{Crawford2015UniquenessRF,
  title={Uniqueness regime for Markov dynamics on quantum lattice spin systems},
  author={Nick Crawford and Wojciech de Roeck and Marius Sch{\"u}tz},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2015},
  volume={48}
}
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. 

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