Decoherence and Quantum-Classical Master Equation Dynamics

TL;DR

This paper investigates conditions under which quantum-classical Liouville dynamics can be simplified to a master equation, introducing a Markovian approximation and a trajectory-based approach to model decoherence in quantum-classical systems.

Contribution

It derives a Markovian master equation for quantum-classical systems and introduces a trajectory method to account for decoherence effects due to the bath.

Findings

Rapid decay of memory kernel justifies Markovian approximation

Trajectory approach effectively models decoherence in quantum-classical dynamics

Application to nonadiabatic chemical reaction rate calculation

Abstract

The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered. Starting with an exact non-Markovian equation for the diagonal elements of the density matrix, an evolution equation for the subsystem density matrix is derived. One contribution to this equation contains the bath average of a memory kernel that accounts for all coherences in the system. It is shown to be a rapidly decaying function, motivating a Markovian approximation on this term in the evolution equation. The resulting subsystem density matrix equation is still non-Markovian due to the fact that bath degrees of freedom have been projected out of the dynamics. Provided the computation of non-equilibrium average values or correlation functions is considered, the non-Markovian character of this equation can be removed by lifting the equation into the full phase space of the system. This leads to a trajectory description of the dynamics where each fictitious trajectory accounts for decoherence due to the bath degrees of freedom. The results are illustrated by computations of the rate constant of a model nonadiabatic chemical reaction.