Generalized Quantum Master Equations In and Out of Equilibrium: When Can One Win?

TL;DR

This paper analyzes the conditions under which generalized quantum master equations (GQMEs) improve simulation accuracy or efficiency, providing exact expressions for memory kernels and clarifying when GQME methods are advantageous in equilibrium and non-equilibrium systems.

Contribution

It derives exact expressions for memory kernels in GQMEs and identifies conditions where GQME approaches match or surpass direct simulation accuracy.

Findings

Exact memory kernel expressions for equilibrium and non-equilibrium systems.

Conditions where GQME yields identical results to direct simulation.

Insights into when GQME methods can improve simulation efficiency or accuracy.

Abstract

Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach seems to offer no advantage over a direct evaluation of the property of interest. Here we provide a more detailed understanding of the conditions under which these methods will offer benefits. In particular, we derive exact expressions for the memory kernel for systems both in and out of equilibrium, and show the conditions under which these expressions will be guaranteed to return a result identical to that obtained from direct simulation. We also show the conditions which approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These exact analytical results thus provide new insights as to when proceeding via the GQME approach can improve the accuracy or efficiency of simulations.