Diffusion and Trapping on a one-dimensional lattice

TL;DR

This paper investigates a one-dimensional lattice model where particles experience both random barriers and traps, revealing complex behaviors and broad survival probability distributions through numerical and analytical methods.

Contribution

It introduces a detailed analysis of combined disorder and trapping effects in 1D, suggesting a potential super universal class for trapping-dominated systems.

Findings

Survival probability follows a broad, log-normal distribution.

Rich behaviors observed typically associated with higher dimensions.

Analytical and numerical methods confirm complex trapping dynamics.

Abstract

The properties of a particle diffusing on a one-dimensional lattice where at each site a random barrier and a random trap act simultaneously on the particle are investigated by numerical and analytical techniques. The combined effect of disorder and traps yields a decreasing survival probability with broad distribution (log-normal). Exact enumerations, effective-medium approximation and spectral analysis are employed. This one-dimensional model shows rather rich behaviours which were previously believed to exist only in higher dimensionality. The possibility of a trapping-dominated super universal class is suggested.