Universal fluctuations in subdiffusive transport

TL;DR

This paper demonstrates that in subdiffusive transport within tilted washboard potentials, the scaled subvelocity follows a universal Levy-stable distribution, independent of potential details or bias strength, due to weak ergodicity breaking.

Contribution

It introduces a universal law for subvelocity fluctuations in subdiffusive systems, linking them to the Levy-stable distribution based on the subdiffusion index and mean subvelocity.

Findings

Scaled subvelocity obeys a Levy-stable distribution.

Universal fluctuations are independent of potential form and bias.

Monte Carlo simulations support the analytical theory.

Abstract

Subdiffusive transport in tilted washboard potentials is studied within the fractional Fokker-Planck equation approach, using the associated continuous time random walk (CTRW) framework. The scaled subvelocity is shown to obey a universal law, assuming the form of a stationary Levy-stable distribution. The latter is defined by the index of subdiffusion alpha and the mean subvelocity only, but interestingly depends neither on the bias strength nor on the specific form of the potential. These scaled, universal subvelocity fluctuations emerge due to the weak ergodicity breaking and are vanishing in the limit of normal diffusion. The results of the analytical heuristic theory are corroborated by Monte Carlo simulations of the underlying CTRW.