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

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 $Ω$ normal temperature dependence of the diffusivity is restored at low enough temperatures, $T<T_\textrm{TAD}(Ω)$ --- in contrast with the problem with constant external forcing. At fixed temperature at small forcing frequency the diffusivity either slowly decreases with $Ω$, or (at stronger forcing) goes through a maximum near $Ω_2$, reciprocal superdiffusion stage duration. At high frequencies, between $Ω_2$ and a fraction of the oscillation frequency at the potential minimum, the diffusivity is shown to decrease with $Ω$ 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.