Non-Markovian Open Quantum Systems

TL;DR

This paper develops a comprehensive framework for non-Markovian quantum dynamics, introducing a canonical dynamical map that captures system-environment correlations and extends traditional Markovian master equations.

Contribution

It introduces a non-Markovian canonical dynamical map and derives a generalized master equation, advancing the understanding of non-Markovian quantum processes.

Findings

Established the relationship between inverse maps and environment correlations.

Derived a non-Markovian master equation beyond Kossakowski-Lindblad form.

Provided a foundation for studying non-equilibrium quantum thermodynamics.

Abstract

We construct a non-Markovian canonical dynamical map that accounts for systems correlated with the environment. The physical meaning of not completely positive maps is studied to obtain a theory of non-Markovian quantum dynamics. The relationship between inverse maps and correlations with the environment is established. A generalized non-Markovian master equation is derived from the canonical dynamical map that goes beyond the Kossakowski-Lindblad Markovian master equation. Non-equilibrium quantum thermodynamics can be be studied within this theory.