A multi-band semiclassical model for surface hopping quantum dynamics

TL;DR

This paper develops a semiclassical surface hopping model using Wigner transform and Weyl quantization to accurately simulate quantum non-adiabatic transitions across potential energy surfaces, especially near avoided crossings.

Contribution

It introduces a novel approach evolving the entire Wigner matrix, including off-diagonal elements, to model non-adiabatic quantum transitions more effectively.

Findings

The model captures non-adiabatic transitions like Berry connection.

Numerical experiments validate the accuracy of the proposed model.

The approach addresses limitations of previous adiabatic-based methods.

Abstract

In the paper we derive a semiclassical model for surface hopping allowing quantum dynamical non-adiabatic transition between different potential energy surfaces in which cases the classical Born-Oppenheimer approximation breaks down. The model is derived using the Wigner transform and Weyl quantization, and the central idea is to evolve the entire Wigner matrix rather than just the diagonal entries as was done previously in the adiabatic case. The off-diagonal entries of the Wigner matrix suitably describe the non-adiabatic transition, such as the Berry connection, for avoided crossings. We study the numerical approximation issues of the model, and then conduct numerical experiments to validate the model.