Enhanced diffusion with abnormal temperature dependence in underdamped space-periodic systems subject to time-periodic driving

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.

Noise-induced rectification in out-of-equilibrium structures

“…Effective diffusion coefficient as a function of dimensionless temperature. We observe the estimated Deff from numerical simulations of the stochastic differential equation (1) using the parameter values p = 0.25, F = 0.96 and T = 5.16.The inset shows that the diffusion coefficient does not behaves monotonically with the temperature, which is counterintuitive phenomenon previously found in other systems (see for example Refs [9,[27][28][29][30]…”

“…This phenomenon is important in the sense that it implies a counterintuitive behavior of the particles diffusing in a medium. To be precise, in recent years it has been shown that, in some systems out of equilibrium, an increase in temperature does not implies always an increase in the diffusion coefficient [9,[27][28][29][30][31][32]. In Fig.…”

“…Q(a m−1 , a m ). (30) where the summation runs over all possible "states" of the Markov chain, i.e., over all possible monomer types. With these expressions it is possible to calculate the following averages,…”

“…7 we display the behavior of the diffusion coefficient Deff with respect to the dimensionless temperature θ, maintaining fixed the The inset shows that the diffusion coefficient does not behaves monotonically with the temperature, which is counterintuitive phenomenon previously found in other systems (see for example Refs. [9,[27][28][29][30]). The occurrence is mainly due an interplay between the noisy and the deterministic dynamics as it has been observed in [9].…”

Diffusion Temperature Dependence in Tilted Periodic Potentials Ranging from Underdamped Systems to Overdamped Systems

“…В работе [30] в определенном интервале приложенных внешних сил. Этот явление авторы назвали температурно-аномальной диффузией (ТАД) [33][34]. Феномен ТАД связан со слабым нарушением эргодичности в таких системах, поскольку время корреляции экспоненциально стремится к бесконечности при 0 → T .…”