Quantum mechanical averaging over fluctuating rates

Abstract

Quantum transport in a fluctuating medium is often described using phenomenological time-dependent model Hamiltonians. Fitting the spectrum of the time-dependent forces onto a collection of oscillators, medium fluctuations can be mapped onto an interaction with a harmonic bath. In this framework, classical as well as quantum mechanical schemes can be applied to estimate averaged transport rates. Considering a generic two state model, a classical approach which relates a transfer rate to each fluctuation, and the total rate to an ensemble average, is shown to reproduce a standard rate expression. This expression turns out to be the high temperature limit of a quantum averaging scheme, which deviates from the classical result at finite temperature. The quantum averaging over fluctuating parameters is proposed here as an efficient and general approach to estimate the validity of quantum-classical simulations which treat quantum transport within an ensemble of molecular configurations generated by classical molecular dynamics.