Asymptotic analysis of diabatic surface hopping algorithm in the adiabatic and non-adiabatic limits

TL;DR

This paper provides an asymptotic analysis of a diabatic surface hopping algorithm, justifying its correct transition rate scaling in the Marcus regime and revealing its mean-field behavior in the adiabatic limit.

Contribution

It offers the first theoretical justification for the diabatic surface hopping algorithm's transition rates and asymptotic behavior across different coupling regimes.

Findings

Correct scaling in Marcus regime for spin-boson model

Conditions ensuring algorithm correctness for general potentials

Mean-field type asymptotic behavior in strong-coupling regime

Abstract

Surface hopping algorithms, as an important class of quantum dynamics simulation algorithms for non-adiabatic dynamics, are typically performed in the adiabatic representation, which can break down in the presence of ill-defined adiabatic potential energy surfaces (PESs) and adiabatic coupling term. Another issue of surface hopping algorithms is the difficulty in capturing the correct scaling of the transition rate in the Marcus (weak-coupling/non-adiabatic) regime. Though the first issue can be circumvented by exploiting the diabatic representation, diabatic surface hopping algorithms usually lack justification on the theoretical level. We consider the diabatic surface hopping algorithm proposed in [Fang, Lu. Multiscale Model. Simul. 16:4, 1603-1622, 2018] and provide the asymptotic analysis of the transition rate in the Marcus regime that justifies the correct scaling for the spin-boson model. We propose two conditions that guarantee the correctness for general potentials. In the opposite (strong-coupling/adiabatic) regime, we derive the asymptotic behavior of the algorithm that interestingly matches a type of mean-field description. The techniques used here may shed light on the analysis for other diabatic-based algorithms.