Introduction to the theory of open quantum systems

TL;DR

This paper provides a comprehensive, self-contained introduction to open quantum systems, emphasizing a novel quasi-stochastic approach and super-quasi-cumulant expansion for describing system dynamics, suitable as a textbook or course material.

Contribution

It introduces a new quasi-stochastic representation of environmental effects and develops a super-quasi-cumulant expansion for open system dynamics, enhancing perturbation theory methods.

Findings

New quasi-stochastic environmental representation

Super-quasi-cumulant expansion for dynamical maps

Practical perturbation theory framework

Abstract

This manuscript is an edited and refined version of the lecture script for a one-semester graduate course given originally at the PhD school in the Institute of Physics of Polish Academy of Sciences in the Spring/Summer semester of 2022. The course expects from the student only a basic knowledge on graduate-level quantum mechanics. The script itself is largely self-contained and could be used as a textbook on the topic of open quantum systems. The program of this course is based on a novel approach to the description of the open system dynamics: It is showed how the environmental degrees of freedom coupled to the system can be represented by a multi-component quasi-stochastic process. Using this representation one constructs the super-quasi-cumulant (or super-qumulant) expansion for the system's dynamical map -- a parametrization that naturally lends itself for the development of a robust and practical perturbation theory. Thus, even an experienced researcher might find this manuscript of some interest.