Diffusion Enhancement in a Periodic Potential under High-Frequency Space-Dependent Forcing

TL;DR

This paper investigates how high-frequency, space-dependent periodic forces influence the long-term diffusion and transport properties of Brownian particles in periodic potentials, revealing significant diffusion enhancement and effective potential modifications.

Contribution

It extends Kapitsa's analysis to include space-dependent forcing, deriving new effective potentials and demonstrating their impact on diffusion and current in Brownian systems.

Findings

Significant increase in diffusion coefficient due to space-dependent forcing

Excellent agreement between numerical results and theoretical predictions

Enhanced transport properties in ratchet potentials

Abstract

We study the long-time behavior of underdamped Brownian particle moving through a viscous medium and in a systematic potential, when it is subjected to a space-dependent high-frequency periodic force. When the frequency is very large, much larger than all other relevant system-frequencies, there is a Kapitsa time-window wherein the effect of frequency dependent forcing can be replaced by a static effective potential. Our new analysis includes the case when the forcing, in addition to being frequency-dependent, is space-dependent as well. The results of the Kapitsa analysis then lead to additional contributions to the effective potential. These are applied to the numerical calculation of the diffusion coefficient (D) for a Brownian particle moving in a periodic potential. Presented are numerical results, which are in excellent agreement with theoretical predictions and which indicate a significant enhancement of D due to the space-dependent forcing terms. In addition we study the transport property (current) of underdamped Brownian particles in a ratchet potential.