Non-Gaussian Normal Diffusion in a Fluctuating Corrugated Channel

TL;DR

This paper investigates the diffusion behavior of a Brownian particle in a fluctuating corrugated channel, revealing non-Gaussian distributions at intermediate times and confirming normal diffusion at long times through analytical methods.

Contribution

It provides an analytical explanation for non-Gaussian diffusion in a simple model, aligning with recent experimental and numerical findings in complex systems.

Findings

Gaussian distribution at short and long times

Exponential distribution at intermediate times

Normal diffusion with a consistent diffusion constant

Abstract

A Brownian particle floating in a narrow corrugated (sinusoidal) channel with fluctuating cross section exhibits non-Gaussian normal diffusion. Its displacements are distributed according to a Gaussian law for very short and asymptotically large observation times, whereas a robust exponential distribution emerges for intermediate observation times of the order of the channel fluctuation correlation time. For intermediate to large observation times the particle undergoes normal diffusion with one and the same effective diffusion constant. These results are analytically interpreted without having recourse to heuristic assumptions. Such a simple model thus reproduces recent experimental and numerical observations obtained by investigating complex biophysical systems.