A resolution of quantum dynamical semigroups

TL;DR

This paper introduces a framework for analyzing quantum dissipative systems using projections that are recurrent or metastable, providing a new way to decompose the dynamics of quantum semigroups.

Contribution

It defines recurrent and metastable projections for quantum dynamical semigroups and proves a decomposition of the identity into these projections.

Findings

Decomposition of the unit operator into recurrent and metastable projections.

Introduction of a notion of recurrence and metastability in quantum dynamics.

Framework applicable to quantum dissipative systems governed by completely positive maps.

Abstract

We consider a class of quantum dissipative systems governed by a one parameter completely positive maps on a von-Neumann algebra. We introduce a notion of recurrent and metastable projections for the dynamics and prove that the unit operator can be decomposed into orthogonal projections where each projections are recurrent or metastable for the dynamics.