Trace distance ergodicity for quantum Markov semigroups
Mathematical Physics
2024-02-06 v2 Statistical Mechanics
math.MP
Representation Theory
Abstract
We discuss the quantitative ergodicity of quantum Markov semigroups in terms of the trace distance from the stationary state, providing a general criterion based on the spectral decomposition of the Lindblad generator. We then apply this criterion to the bosonic and fermionic Ornstein-Uhlenbeck semigroups and to a family of quantum Markov semigroups parametrized by semisimple Lie algebras and their irreducible representations, in which the Lindblad generator is given by the adjoint action of the Casimir element.
Cite
@article{arxiv.2206.11923,
title = {Trace distance ergodicity for quantum Markov semigroups},
author = {Lorenzo Bertini and Alberto De Sole and Gustavo Posta},
journal= {arXiv preprint arXiv:2206.11923},
year = {2024}
}