On the structure of quantum Markov semigroups of weak coupling limit type

J R Bolaños-Servín,F Fagnola

doi:10.1088/1742-6596/819/1/012003

Abstract

We discuss some recent results on the structure of quantum Markov semigroups of weak coupling limit type and their stationary states. In particular, we identify the minimal central projection in the fixed point algebra where they act in a trivial way and show, when they admit a single Bohr frequency, that all invariant states are convex combinations of equilibrium states and arbitrary states supported in the above minimal central projection.

Highlights

Quantum Markov Semigroups (QMS) or, in the physical terminology, quantum dynamical semigroups are the fundamental tool for mathematical modelling of open quantum systems interacting with external environments
In [1] we began the study of invariant states of QMS of weak coupling limit type (WCLT) trying to single out special subclasses of invariant states with properties that are rich enough to go beyond the equilibrium situation and possibly allow explicit solutions
Following a suggestion emerging in that work, non-equilibrium states seem to be those which are a function of the system Hamiltonian HS

Summary

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Introduction

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