Analysis of the Forward-Backward Trajectory Solution for the Mixed Quantum-Classical Liouville Equation

TL;DR

This paper analyzes the forward-backward trajectory solution for the mixed quantum-classical Liouville equation, assessing its properties, validity, and utility, and introduces an extension called the jump forward-backward trajectory solution for systematic improvement.

Contribution

It provides a detailed analysis of the forward-backward trajectory method and introduces a new extension to enhance its accuracy in simulating quantum processes.

Findings

The original forward-backward trajectory solution has specific properties and limitations.

The jump extension systematically improves the accuracy of the solution.

Numerical tests validate the effectiveness of the extended method.

Abstract

Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping basis [J. Chem. Phys. 137, 22A507 (2012)] is one such scheme. It simulates the dynamics via the propagation of forward and backward trajectories of quantum coherent state variables, and the propagation of bath trajectories on a mean-field potential determined jointly by the forward and backward trajectories. An analysis of the properties of this solution, numerical tests of its validity and an investigation of its utility for the study of nonadiabtic quantum processes are given. In addition, we present an extension of this approximate solution that allows one to systematically improve the results. This extension, termed the jump forward-backward trajectory solution, is analyzed and tested in detail and its various implementations are discussed.