Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations

TL;DR

This paper demonstrates that Gaussian random potentials with decaying correlations cause persistent, ultraslow logarithmic diffusion at low temperatures, revealing complex crossover behaviors and non-ergodic features in subdiffusive dynamics.

Contribution

It uncovers a universal ultraslow diffusion mechanism in stationary Gaussian potentials with decaying correlations, supported by simulations and a scaling theory.

Findings

Ultraslow logarithmic diffusion occurs at low temperatures in such potentials.

Crossover from ultraslow to power-law and then to normal diffusion with increasing temperature.

Ultraslow diffusion is faster than the de Gennes-Baessler-Zwanzig limit and exhibits non-ergodicity.

Abstract

Logarithmic or Sinai type subdiffusion is usually associated with random force disorder and non-stationary potential fluctuations whose root mean squared amplitude grows with distance. We show here that extremely persistent, macroscopic ultraslow logarithmic diffusion also universally emerges at sufficiently low temperatures in stationary Gaussian random potentials with spatially decaying correlations, known to exist in a broad range of physical systems. Combining results from extensive simulations with a scaling approach we elucidate the physical mechanism of this unusual subdiffusion. In particular, we explain why with growing temperature and/or time a first crossover occurs to standard, power-law subdiffusion, with a time-dependent power law exponent, and then a second crossover occurs to normal diffusion with a disorder-renormalized diffusion coefficient. Interestingly, the initial, nominally ultraslow diffusion turns out to be much faster than the universal de Gennes-Baessler-Zwanzig limit of the renormalized normal diffusion, which physically cannot be attained at sufficiently low temperatures and/or for strong disorder. The ultraslow diffusion is also non-ergodic and displays a local bias phenomenon. Our simple scaling theory not only explains our numerical findings, but qualitatively has also a predictive character.