Quasiclassical approaches to the generalized quantum master equation

TL;DR

This paper investigates the use of approximate solutions to the generalized quantum master equation (GQME) with quasiclassical methods, comparing Ehrenfest mean-field theory and spin mapping for spin-boson models, highlighting the superior performance of spin mapping.

Contribution

It introduces and compares two methods for calculating memory kernels in GQME using quasiclassical trajectories, demonstrating the effectiveness of spin mapping over Ehrenfest.

Findings

Spin mapping outperforms Ehrenfest in accuracy across models.

Coupling spin mapping with a master equation resolves negative population issues.

GQME accuracy depends strongly on the kernel calculation technique.

Abstract

The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels which are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper we study the approximate solution of the GQME, obtained by calculating the kernels with two methods, namely Ehrenfest mean-field theory and spin mapping. We test the approaches on a range of spin--boson models with increasing energy bias between the two electronic levels and place a particular focus on the long-time limits of the populations. We find that the accuracy of the predictions of the GQME depends strongly on the specific technique used to calculate the kernels. In particular, spin mapping outperforms Ehrenfest for all systems studied. The problem of unphysical negative electronic populations affecting spin mapping is resolved by coupling the method with the master equation. Conversely, Ehrenfest in conjunction with the GQME can predict negative populations, despite the fact that the populations calculated from direct dynamics are positive definite.