Quantum Kramers' equation for energy diffusion and barrier crossing dynamics in the low friction regime

TL;DR

This paper extends the quantum Kramers' equation to the low friction regime, providing a comprehensive quantum rate theory for barrier crossing that accounts for quantum effects at all orders and is valid across all temperatures.

Contribution

It develops a non-Markovian quantum Kramers' equation in energy space for the weak friction regime, independent of path integral methods, and applicable at arbitrary temperatures.

Findings

Quantum rate can be reduced below classical values depending on potential.

The theory is valid for arbitrary temperature and noise correlation.

It accounts for quantum effects to all orders.

Abstract

Based on a true phase space probability distribution function and an ensemble averaging procedure we have recently developed [Phys. Rev. E 65, 021109 (2002)] a non-Markovian quantum Kramers' equation to derive the quantum rate coefficient for barrier crossing due to thermal activation and tunneling in the intermediate to strong friction regime. We complement and extend this approach to weak friction regime to derive quantum Kramers' equation in energy space and the rate of decay from a metastable well. The theory is valid for arbitrary temperature and noise correlation. We show that depending on the nature of the potential there may be a net reduction of the total quantum rate below its corresponding classical value which is in conformity with earlier observation. The method is independent of path integral approaches and takes care of quantum effects to all orders.