An introduction to Markovian open quantum systems

TL;DR

This paper provides a clear, educational overview of Markovian open quantum systems, covering the Lindblad equation, stochastic trajectories, steady states, and physical phenomena arising from nonunitary dynamics, aimed at newcomers and researchers.

Contribution

It offers a pedagogical introduction with conceptual explanations, examples, and exercises to help readers understand the mathematical and physical foundations of Markovian open quantum systems.

Findings

Explanation of Lindblad equation and its physical origins

Illustration of stochastic pure-state trajectories and measurement protocols

Discussion of steady states and nonunitary phenomena

Abstract

This is a concise, pedagogical introduction to the dynamic field of open quantum systems governed by Markovian master equations. We focus on the mathematical and physical origins of the widely used Lindblad equation, its unraveling in terms of stochastic pure-state trajectories and the corresponding continuous measurement protocols, the structure of steady states with emphasis on the role of symmetry and conservation laws, and a sampling of the novel physical phenomena that arise from nonunitary dynamics (dissipation and measurements). This is far from a comprehensive summary of the field. Rather, the objective is to provide a conceptual foundation and physically illuminating examples that are useful to graduate students and researchers entering this subject. There are exercise problems and references for further reading throughout the notes.