On the Generalized Kramers Problem with Oscillatory Memory Friction

TL;DR

This paper investigates the effects of an oscillatory memory friction on the Kramers problem, revealing a new 'stair-like' decay regime of the transmission coefficient and clarifying behaviors across different parameter regimes.

Contribution

It introduces an oscillatory memory kernel into the Kramers problem and identifies a novel 'stair-like' decay behavior of the transmission coefficient, expanding understanding of reaction dynamics.

Findings

No caging observed with oscillatory memory kernel

Identification of a new 'stair-like' decay regime

Recovery of known regimes in appropriate parameters

Abstract

The time-dependent transmission coefficient for the Kramers problem exhibits different behaviors in different parameter regimes. In the high friction regime it decays monotonically ("non-adiabatic"), and in the low friction regime it decays in an oscillatory fashion ("energy-diffusion-limited"). The generalized Kramers problem with an exponential memory friction exhibits an additional oscillatory behavior in the high friction regime ("caging"). In this paper we consider an oscillatory memory kernel, which can be associated with a model in which the reaction coordinate is linearly coupled to a nonreactive coordinate, which is in turn coupled to a heat bath. We recover the non-adiabatic and energy-diffusion-limited behaviors of the transmission coefficient in appropriate parameter regimes, and find that caging is not observed with an oscillatory memory kernel. Most interestingly, we identify a new regime in which the time-dependent transmission coefficient decays via a series of rather sharp steps followed by plateaus ("stair-like"). We explain this regime and its dependence on the various parameters of the system.