Perturbative criteria for the ergodicity of interacting dissipative quantum lattice systems

Abstract

We introduce a class of quantum Markov semigroups describing the evolution of interacting quantum lattice systems, specified either as generic qudits or as fermions. The corresponding generators, which include both conservative and dissipative evolutions, are given by the superposition of local generators in the Lindblad form. Under general conditions, we show that the associated infinite volume dynamics is well defined and can be obtained as the strong limit of the finite volume dynamics. By regarding the interacting evolution as a perturbation of a non-interacting dissipative dynamics, we further obtain a quantitative criterion that yields the ergodicity of the quantum Markov semigroup together with the exponential convergence of local observables. The analysis is based on suitable a priori bounds on the resolvent equation which yield quantitive estimates on the evolution of local observables.

References in corpus (9)

• From Classical to Quantum Shannon Theory
• Finite-temperature transport in one-dimensional quantum lattice models
• The Quantum Wasserstein Distance of Order 1
• Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
• Effective quantum Zeno dynamics in dissipative quantum systems
• Quantum spin systems on infinite lattices
• Uniqueness regime for Markov dynamics on quantum lattice spin systems
• The Wasserstein distance of order 1 for quantum spin systems on infinite lattices
• Trace distance ergodicity for quantum Markov semigroups