Coupled forward-backward trajectory approach for non-equilibrium electron-ion dynamics

TL;DR

This paper presents a coupled forward-backward trajectory method for simulating non-equilibrium electron-ion dynamics, improving accuracy over mean field theory by capturing quantum coherence and correlations in nonadiabatic systems.

Contribution

It introduces a novel coupled trajectory ansatz that enhances non-equilibrium electron-ion dynamics simulations beyond traditional mean field approaches.

Findings

Improves simulation accuracy over mean field theory.

Captures quantum coherence and electron-nuclear correlations.

Effective in nonadiabatic regimes beyond perturbative coupling.

Abstract

We introduce a simple ansatz for the wavefunction of a many-body system based on coupled forward and backward-propagating semiclassical trajectories. This method is primarily aimed at, but not limited to, treating nonequilibrium dynamics in electron-phonon systems. The time-evolution of the system is obtained from the Euler-Lagrange variational principle, and we show that this ansatz yields Ehrenfest mean field theory in the limit that the forward and backward trajectories are orthogonal, and in the limit that they coalesce. We investigate accuracy and performance of this method by simulating electronic relaxation in the spin-boson model and the Holstein model. Although this method involves only pairs of semiclassical trajectories, it shows a substantial improvement over mean field theory, capturing quantum coherence of nuclear dynamics as well as electron-nuclear correlations. This improvement is particularly evident in nonadiabatic systems, where the accuracy of this coupled trajectory method extends well beyond the perturbative electron-phonon coupling regime. This approach thus provides an attractive route forward to the ab-initio description of relaxation processes, such as thermalization, in condensed phase systems.