Brownian non-Gaussian diffusion of self-avoiding walks

TL;DR

This study confirms through simulations that critical self-avoiding walks exhibit Brownian motion with non-Gaussian initial displacement distributions, transitioning to Gaussianity over time, aligning with recent theoretical predictions.

Contribution

The paper provides the first simulation validation of the theoretical prediction of Brownian non-Gaussian diffusion in self-avoiding walks without using fitting parameters.

Findings

Mean square displacement grows linearly with time.

Initial probability density is strongly non-Gaussian.

Distribution crosses over to Gaussian at large times.

Abstract

Three-dimensional Monte Carlo simulations provide a striking confirmation to a recent theoretical prediction: the Brownian non-Gaussian diffusion of critical self-avoiding walks. Although the mean square displacement of the polymer center of mass grows linearly with time (Brownian behavior), the initial probability density function is strongly non-Gaussian and crosses over to Gaussianity only at large time. Full agreement between theory and simulations is achieved without the employment of fitting parameters. We discuss simulation techniques potentially capable of addressing the study of anomalous diffusion under complex conditions like adsorption- or Theta-transition.