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
On the structure of quantum Markov semigroups of weak coupling limit type This content has been downloaded from IOPscience. You may be interested in: On translation-covariant quantum Markov equations A S Holevo ON SEMIGROUPS WITH ONE RELATION AND SEMIGROUPS WITHOUT CYCLES G U Oganesyan Ergodic properties of quantum dynamical semigroups P ugiewicz, R Olkiewicz and B Zegarlinski Quantum entropies, Schur concavity and dynamical semigroups Paolo Aniello LATTICE ISOMORPHISMS OF SEMIGROUPSDECOMPOSABLE INTO FREE PRODUCTS OF SZERMOIGROUPSWITH AMALGAMATED V A Baranski Boundary conditions, semigroups, quantum jumps, and the quantum arrow of time Arno Bohm MAXIMAL ATTRACTORS OF SEMIGROUPS CORRESPONDING TO EVOLUTION DIFFERENTIAL EAQVUABTabIOinNaSnd M I Vishik AN ALGORITHM FOR RECOGNIZING THE SOLVABILITY OF EQUATIONSIN ONE UNKNOWN OVER SOEVMERIGLRAOPUOPFSLEWSITSHTHAN 1/3 IN THE DEFINING WORDS V A Osipova Operator stochastic differential equations and stochastic semigroups A V Skorokhod
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