Quantum-Classical Non-Adiabatic Dynamics: Coupled- vs. Independent-Trajectory Methods

TL;DR

This paper introduces a new quantum-classical approach based on coupled trajectories within the exact factorization framework, addressing key issues in mixed quantum-classical dynamics like decoherence and wave packet splitting.

Contribution

It proposes a simple coupled-trajectory scheme that improves upon traditional methods by accurately capturing electron-nuclear interactions and dynamics.

Findings

The new method reproduces quantum wave packet dynamics more accurately.

It overcomes decoherence and wave packet splitting issues.

Validated against full quantum solutions for challenging models.

Abstract

Trajectory-based mixed quantum-classical approaches to coupled electron-nuclear dynamics suffer from well-studied problems such as the lack of (or incorrect account for) decoherence in the trajectory surface hopping method and the inability of reproducing the spatial splitting of a nuclear wave packet in Ehrenfest-like dynamics. In the context of electronic non-adiabatic processes, these problems can result in wrong predictions for quantum populations and in unphysical outcomes for the nuclear dynamics. In this paper we propose a solution to these issues by approximating the coupled electronic and nuclear equations within the framework of the exact factorization of the electron-nuclear wave function. We present a simple quantum-classical scheme based on coupled classical trajectories, and test it against the full quantum mechanical solution from wave packet dynamics for some model situations which represent particularly challenging problems for the above-mentioned traditional methods.