An Analysis of the Mapping Approach to Surface Hopping

TL;DR

This paper analyzes the mapping approach to surface hopping (MASH), demonstrating its unique ability to guarantee correct thermalization and its applicability to multi-time correlation functions, while also exploring extensions like the quantum jump procedure.

Contribution

The paper proves the uniqueness of MASH in guaranteeing thermalization and extends its application to multi-time correlation functions, comparing it with other estimators and techniques.

Findings

MASH guarantees correct thermalisation unlike similar methods.

MASH can compute multi-time correlation functions for 2D spectra.

The quantum jump procedure does not improve MASH results as expected.

Abstract

Recently, the mapping approach to surface hopping (MASH) was proposed as a method to simulate the non-adiabatic dynamics of two-level systems. It was shown that the method possesses many desirable qualities, both theoretically and through numerical simulations. We explain this success by proving that, out of similar mapping methods, MASH dynamics is unique in guaranteeing correct thermalisation, but that many different "estimators" can be used on top of it. We also show that MASH can successfully calculate multi-time correlation functions, which can be used for the simulation of 2D spectra. We also generalise an, in principle more accurate, technique known as the quantum jump procedure to these calculations and show that, contrary to expectations, it does not improve the results.