Temperature-abnormal diffusivity in underdamped space-periodic systems driven by external time-periodic force

TL;DR

This paper investigates how external time-periodic forcing can significantly enhance diffusion in underdamped Brownian particles within a symmetric potential, revealing abnormal temperature dependence and frequency effects.

Contribution

It demonstrates that external periodic forcing can cause large diffusion enhancement and abnormal temperature dependence, with detailed analysis of frequency effects and comparison of forcing types.

Findings

Diffusivity can be enhanced by many orders of magnitude.

Abnormal (decreasing) temperature dependence occurs at high forcing amplitudes.

Diffusivity behavior varies with forcing frequency, showing maxima and power-law decay.

Abstract

We present a study of diffusion enhancement of underdamped Brownian particles in 1D symmetric space-periodic potential due to external symmetric time-periodic forcing with zero mean. We show that the diffusivity can be enhanced by many orders of magnitude at appropriate choice of the forcing amplitude and frequency. The diffusivity demonstrates TAD, abnormal (decreasing) temperature dependence at forcing amplitudes exceeding certain value. At any fixed forcing frequency $\Omega$ normal temperature dependence of the diffusivity is restored at low enough temperatures, $T<T_\textrm{TAD}(\Omega)$ --- in contrast with the problem with constant external forcing. At fixed temperature at small forcing frequency the diffusivity either slowly decreases with $\Omega$, or (at stronger forcing) goes through a maximum near $\Omega_2$, reciprocal superdiffusion stage duration. At high frequencies, between $\Omega_2$ and a fraction of the oscillation frequency at the potential minimum, the diffusivity is shown to decrease with $\Omega$ according to a power law, with exponent related to the transient superdiffusion exponent. This behavior is found similar for the cases of sinusoidal in time and piecewise constant periodic ("square") forcing.