Open Quantum Systems. An Introduction

TL;DR

This paper provides a comprehensive overview of open quantum systems, unifying various approaches and detailing the mathematical structure and derivations of their dynamics, including Markovian and non-Markovian processes.

Contribution

It offers a unified framework for understanding open quantum system dynamics, integrating concepts from different research communities and detailing derivations of dynamical equations.

Findings

Detailed mathematical structure of dynamical maps

Unified approach to Markovian and non-Markovian evolutions

Clarification of concepts across different communities

Abstract

We revise fundamental concepts in the dynamics of open quantum systems in the light of modern developments in the field. Our aim is to present a unified approach to the quantum evolution of open systems that incorporates the concepts and methods traditionally employed by different communities. We present in some detail the mathematical structure and the general properties of the dynamical maps underlying open system dynamics. We also discuss the microscopic derivation of dynamical equations, including both Markovian and non-Markovian evolutions.