Time-dependent barrier passage of Two-dimensional non-Ohmic damping system

TL;DR

This paper investigates how non-Ohmic, memory-dependent damping affects the probability and dynamics of a particle crossing a potential barrier in a two-dimensional system, revealing non-monotonic behaviors and reduced recrossing.

Contribution

It introduces an analytical approach to study time-dependent barrier crossing in 2D non-Ohmic damping systems using the generalized Langevin equation and reactive flux method.

Findings

Non-monotonic dependence of passing probability on the friction exponent

Optimal incident angle varies with memory effects

Higher steady transmission coefficient reduces barrier recrossing

Abstract

The time-dependent barrier passage of an anomalous damping system is studied via the generalized Langevin equation (GLE) with non-Ohmic memory damping friction tensor and corresponding thermal colored noise tensor describing a particle passing over the saddle point of a two-dimensional quadratic potential energy surface. The time-dependent passing probability and transmission coefficient are analytically obtained by using of the reactive flux method. The long memory aspect of friction is revealed to originate a non-monotonic $\delta$(power exponent of the friction) dependence of the passing probability, the optimal incident angle of the particle and the steady anomalous transmission coefficient. In the long time limit a bigger steady transmission coefficient is obtained which means less barrier recrossing than the one-dimensional case.