[Paper Review] Lecture Notes on the Theory of Open Quantum Systems

Daniel A. Lidar|arXiv (Cornell University)|Feb 3, 2019

Quantum Mechanics and Applications6 references96 citations

TL;DR

A self-contained set of graduate lecture notes covering open quantum systems, with focus on completely positive maps and master equations (Markovian and non-Markovian).

ABSTRACT

This is a self-contained set of lecture notes covering various aspects of the theory of open quantum system, at a level appropriate for a one-semester graduate course. The main emphasis is on completely positive maps and master equations, both Markovian and non-Markovian.

Motivation & Objective

• Provide a self-contained introduction to open quantum systems suitable for a one-semester graduate course.
• Explain completely positive maps and their role in describing system dynamics.
• Derive and contrast Markovian and non-Markovian master equations for open quantum systems.

Proposed method

• Systematic exposition of open quantum system theory.
• Derivations of master equations and CP maps.
• In v2, corrections and a simplified derivation of post-Markovian master equations by Haimeng Zhang (p.118).
• Emphasis on conceptual clarity suitable for teaching and learning in a course setting.

Experimental results

Research questions

• RQ1 What is the appropriate formalism (CP maps) to describe the reduced dynamics of an open quantum system?
• RQ2 How are Markovian and non-Markovian master equations derived and interpreted in this framework?
• RQ3 What are the key differences and connections between various master equation approaches?
• RQ4 How can post-Markovian master equations be derived and solved within this theory?

Key findings

• The notes synthesize the theory of open quantum systems focusing on CP maps and master equations.
• They present both Markovian and non-Markovian approaches within a unified framework.
• A revised version fixes corrections and includes a simplified derivation of post-Markovian master equations.
• The material is designed for a one-semester graduate course and is self-contained.