General form of quantum evolution

TL;DR

This paper develops a comprehensive framework for describing the local in time dynamics of open quantum systems, extending the Lindblad form to non-Markovian cases and highlighting the complexity of their generators.

Contribution

It introduces a general representation of local generators for quantum dynamics that encompasses non-Markovian evolution, extending the Lindblad form for Markovian cases.

Findings

Markovian evolution is a special case of non-Markovian dynamics.

The structure of non-Markovian generators is complex and not fully classified.

The paper provides illustrative examples of the proposed approach.

Abstract

We propose a complete treatment of a local in time dynamics of open quantum systems. In this approach Markovian evolution turns out to be a special case of a general non-Markovian one. We provide a general representation of the local generator which generalizes well known Lindblad representation for the Markovian dynamics. It shows that the structure of non-Markovian generators is highly intricate and the problem of their classification is still open. Simple examples illustrate our approach.