Is Lindblad for me?

TL;DR

This review critically examines the Lindblad master equation's validity in modeling open quantum systems, providing practical guidelines and case studies to identify its limitations in modern research contexts.

Contribution

It offers a detailed analysis of the standard approximations of the Lindblad equation and presents a checklist to assess its applicability in various quantum systems.

Findings

Re-examination of Born, Markov, and Rotating Wave approximations.

Case studies illustrating the breakdown of Lindblad assumptions.

A practical checklist for applicability assessment.

Abstract

The Lindblad master equation is a foundational tool for modeling the dynamics of open quantum systems. As its use has extended far beyond its original domain, the boundaries of its validity have grown opaque. In particular, the rise of new research areas including open quantum many-body systems, non-equilibrium condensed matter, and the possibility to test its limits in driven-open quantum simulators, call for a critical revision of its regimes of applicability. In this pedagogical review, we re-examine the folklore surrounding its three standard approximations (Born, Markov, and Rotating Wave Approximation), as we build our narrative by employing a series of examples and case studies accessible to any reader with a solid background on the fundamentals of quantum mechanics. As a synthesis of our work, we offer a checklist that contrasts common lore with refined expectations, offering a practical guideline for assessing the breakdown of the Lindblad framework in the problem at hand.