Strong Frequency Dependence in Over-damped Systems

TL;DR

This paper investigates unusual frequency-dependent behavior in over-damped systems, revealing a phenomenon akin to stochastic resonance caused by boundary-driven oscillations, supported by analytical and simulation results.

Contribution

It demonstrates a novel frequency dependence in over-damped systems due to boundary effects, linking continuous and discrete models through analysis and simulation.

Findings

Amplitude oscillates with frequency in boundary-driven over-damped systems

Monte Carlo simulations confirm the phenomenon in TASEP model

Comparison shows consistent behavior in both analytical and simulation approaches

Abstract

Strong frequency dependence is unlikely in diffusive or over-damped systems. When exceptions do occur, such as in the case of stochastic resonance, it signals an interesting underlying phenomenon. We find that such a case appears in the motion of a particle in a diffusive environment under the effect of periodically oscillating retarded force emanating from the boundaries. The amplitude for the expectation value of position has an oscillating frequency dependence, quite unlike a typical resonance. We first present an analysis of the associated Fokker-Planck equation, then report the results of a Monte Carlo simulation of the effect of a periodic perturbation on a totally asymmetric simple exclusion process (TASEP) model with single species. This model is known to exhibit a randomly moving shock profile, dynamics of which is a discrete realization of the Fokker-Planck equation. Comparison of relevant quantities from the two analyses indicate that the same phenomenon is apparent in both systems.