Non-Gaussian normal diffusion induced by delocalization

TL;DR

This paper demonstrates through simulations that non-Gaussian normal diffusion, characterized by a non-Gaussian PDF and linear MSD, can occur in energy transport along disordered lattices at finite temperatures due to mode delocalization.

Contribution

The study reveals that nonlinear interactions induce delocalization of localized modes, leading to non-Gaussian normal diffusion in one-dimensional disordered lattices.

Findings

Energy-density fluctuations become delocalized with nonlinear interactions.

Non-Gaussian PDFs are observed during energy relaxation.

Linear MSD dependence on time indicates normal diffusion.

Abstract

The non-Gaussian normal diffusion, i.e., the probability distribution function (PDF) is non-Gaussian but the mean squared displacement (MSD) depends on time linearly, has been observed in particle motions. Here we show by numerical simulations that this phenomenon may manifest in energy diffusion along lattices at a non-zero, finite temperature. The model we study is one-dimensional disordered lattices with on-site potential. We find that the energy-density fluctuations are spatially localized if the nonlinear interaction is suppressed, but may relax with a non-Gaussian PDF and a linear time-dependent MSD when the nonlinear interaction is turned on. Our analysis suggests that the mechanism lies in the delocalization properties of the localized modes.