On the Generalized Kramers Problem with Exponential Memory Friction

TL;DR

This paper extends the analysis of the Kramers problem with exponential memory friction to include low-friction regimes, providing a unified theoretical framework and validating results through numerical simulations.

Contribution

It generalizes existing methods to exponential memory kernels in the low-friction regime, complementing prior high-friction analyses.

Findings

Theoretical results agree with numerical simulations.

Unified approach for different friction regimes.

Extension to exponential memory kernels.

Abstract

The time-dependent transmission coefficient for the generalized Kramers problem with exponential memory friction has recently been calculated by Kohen and Tannor [D. Kohen and D. J. Tannor, J. Chem. Phys. Vol. 103, 6013 (1995)] using a procedure based on the method of reactive flux and the phase space distribution function. Their analysis is restricted to the high friction regime or diffusion-limited regime. We recently developed a complementary theory for the low-friction energy-diffusion-limited regime in the Markovian limit [Sancho et al., cond-mat/9806001, to appear in J. Chem. Phys.]. Here we generalize our method to the case of an exponential dissipative memory kernel. We test our results, as well as those of Kohen and Tannor, against numerical simulations.