Diffusion and superdiffusion in lattice models of colliding particles with stored momentum

TL;DR

This paper introduces lattice models of colliding particles with stored momentum, analyzing their diffusive behavior across different dimensions, revealing superdiffusion in one and two dimensions under specific conditions, and standard diffusion in three or more dimensions.

Contribution

The paper presents new discrete models of particles with stored momentum and characterizes their diffusive properties across various dimensions, including superdiffusive behavior in low dimensions.

Findings

Superdiffusive behavior in one dimension with power law correction.

Superdiffusivity in two dimensions with logarithmic correction for certain initial conditions.

Diffusive behavior in three or higher dimensions.

Abstract

We introduce two discrete models of a collection of colliding particles with stored momentum and study the asymptotic growth of the mean-square displacement of an active particle. We prove that the models are superdiffusive in one dimension (with power law correction) and diffusive in three and higher dimensions. In two dimensions we demonstrate superdiffusivity (with logarithmic correction) for certain anisotropic initial conditions.