Surface-hopping dynamics and decoherence with quantum equilibrium structure

TL;DR

This paper investigates conditions under which quantum-classical Liouville dynamics can be simplified to surface-hopping models, focusing on decoherence, initial state sampling, and the validity of Markovian approximations in open quantum systems.

Contribution

It provides a theoretical framework for when surface-hopping dynamics accurately approximate quantum-classical evolution, considering initial state sampling and decoherence effects.

Findings

Surface-hopping reduction is valid with quantum or classical bath initial sampling.

Markovian approximation validity depends on initial state and coherence considerations.

Reduction may not be possible when only quantum dispersion is averaged.

Abstract

In open quantum systems decoherence occurs through interaction of a quantum subsystem with its environment. The computation of expectation values requires a knowledge of the quantum dynamics of operators and sampling from initial states of the density matrix describing the subsystem and bath. We consider situations where the quantum evolution can be approximated by quantum-classical Liouville dynamics and examine the circumstances under which the evolution can be reduced to surface-hopping dynamics, where the evolution consists of trajectory segments evolving exclusively on single adiabatic surfaces, with probabilistic hops between these surfaces. The justification for the reduction depends on the validity of a Markovian approximation on a bath averaged memory kernel that accounts for quantum coherence in the system. We show that such a reduction is often possible when initial sampling is from either the quantum or classical bath initial distributions. If the average is taken only over the quantum dispersion that broadens the classical distribution, then such a reduction is not always possible.