Dynamical Semigroups for Unbounded Repeated Perturbation of Open System

TL;DR

This paper proves the existence of unique, trace-preserving dynamical semigroups for open quantum systems with unbounded generators, advancing understanding of their mathematical structure and state evolution.

Contribution

It establishes the existence and properties of minimal dynamical semigroups for unbounded generators in open quantum systems, including their dual automorphisms and action on states.

Findings

Existence of unique minimal trace-preserving semigroups

Dual system is unital quasi-free and completely positive

Analysis of dynamical action on quasi-free states

Abstract

We consider dynamical semigroups with unbounded Kossakowski-Lindblad-Davies generators which are related to evolution of an open system with a tuned repeated harmonic perturbation. Our main result is the proof of existence of uniquely determined minimal trace-preserving strongly continuous dynamical semigroups on the space of density matrices. The corresponding dual W *-dynamical system is shown to be unital quasi-free and completely positive automorphisms of the CCR-algebra. We also comment on the action of dynamical semigroups on quasi-free states.