Universal Fluctuations of Single-Particle Diffusivity in Quenched Environment

TL;DR

This paper demonstrates that in disordered systems, the distribution of single-particle diffusivity follows a universal inverse Levy distribution across dimensions, highlighting significant non-self-averaging effects and confinement influences.

Contribution

It introduces the universal inverse Levy distribution for diffusivity in quenched disordered systems, applicable across different dimensions, and analyzes the effects of sample fluctuations and confinement.

Findings

Diffusivity distribution is universal and follows an inverse Levy distribution.

Fluctuations in diffusivity surpass those predicted by annealed theory.

Confinement significantly affects single-particle diffusivity.

Abstract

Local diffusion coefficients in disordered materials such as living cells are highly heterogeneous. Quenched disorder is utilized substantially to study such complex systems, whereas its analytical treatment is difficult to handle. We consider finite systems with quenched disorder in order to investigate the effects of sample disorder fluctuations and confinement on single-particle diffusivity. While the system is ergodic in a single disorder realization, the time-averaged mean squared displacement depends on the disorder, i.e., the system is ergodic but non-self-averaging. We find that the inverse Levy distribution is a universal distribution for diffusivity in the sense that it can be applied for arbitrary dimensions. Quantifying the degree of the non-self-averaging effect, we show that fluctuations of single-particle diffusivity far exceed the corresponding annealed theory and also find confinement effects. The relevance for experimental situations is also discussed.