No 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 < TTAD(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 Ω2, reciprocal superdiffusion stage duration. At high frequencies, between Ω2 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. PACS numbers: 05.40.-a, 02.50.Ey, 68.43.Jk, 66.30.J-* azhiglo@uchicago.edu ular gas [9]. It turned possible to increase the diffusivity of ions in membrane channels by varying the external electromagnetic field [10]. One can increase the rates of diffusion-limited physical processes, and effectively separate micro-and nano-particles of different nature by varying diffusion coefficients in different directions [11].Despite these remarkable achievements, quantitative description of such enhanced diffusion under the influence of external forces remains fragmentary to date.

No abstract