Strong Frequency Dependence in Over-damped Systems

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.