Analysis of quantum semigroups with GKS--Lindblad generators II. General

TL;DR

This paper provides a comprehensive analysis of quantum semigroups with GKS--Lindblad generators, detailing their structure, stationary states, asymptotic behavior, and perturbation effects in finite-dimensional open quantum systems.

Contribution

It extends the characterization of Lindblad generators, explores invariant operators and symmetries, and discusses perturbation theory with detailed examples.

Findings

Complete set of stationary states identified

Asymptotic behavior of quantum evolutions characterized

Invariant operators and symmetries analyzed

Abstract

Semigroups describing the time evolution of open quantum systems in finite-dimensional spaces have generators of a special form, known as Lindblad generators. These generators and the corresponding processes of time evolution are analyzed, characterized as Decay, Dissipation and Dephasing. In relation to these processes the Hilbert space of the system is equipped with a special structure, a decomposition into a sum of mutually orthogonal subspaces. The complete set of all the stationary states and the asymptotic behavior of the evolutions are presented in detail. Some unusual special facts about invariant operators and symmetries are studied, examples are demonstrated. Perturbation theory for the structure and for the stationary states is discussed and performed in case studies.