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.

Trace distance ergodicity for quantum Markov semigroups / Bertini, Lorenzo; De Sole, Alberto; Posta, Gustavo. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 286:7(2024). [10.1016/j.jfa.2024.110340]

Trace distance ergodicity for quantum Markov semigroups

Bertini, Lorenzo;De Sole, Alberto;Posta, Gustavo
2024

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.
2024
Quantum Markov semigroups; Trace distance; Rate of convergence to equilibrium; Casimir operator
01 Pubblicazione su rivista::01a Articolo in rivista
Trace distance ergodicity for quantum Markov semigroups / Bertini, Lorenzo; De Sole, Alberto; Posta, Gustavo. - In: JOURNAL OF FUNCTIONAL ANALYSIS. - ISSN 0022-1236. - 286:7(2024). [10.1016/j.jfa.2024.110340]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1700929
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