Brownian walkers within subdiffusing territorial boundaries

TL;DR

This paper models the movement of a Brownian particle within subdiffusing boundaries, deriving exact MSD expressions and revealing non-monotonic diffusion phenomena under certain conditions.

Contribution

It introduces an analytically tractable model for a Brownian walker in subdiffusing boundaries, extending known results and uncovering new transient negative diffusion effects.

Findings

Exact MSD calculations for subdiffusing boundaries

Identification of non-monotonic MSD behavior

Discovery of transient negative diffusion phenomena

Abstract

Inspired by the collective phenomenon of territorial emergence, whereby animals move and interact through the scent marks they deposit, we study the dynamics of a 1D Brownian walker in a random environment consisting of confining boundaries that are themselves diffusing anomalously. We show how to reduce, in certain parameter regimes, the non-Markovian, many-body problem of territoriality to the analytically tractable one-body problem studied here. The mean square displacement (MSD) of the 1D Brownian walker within subdiffusing boundaries is calculated exactly and generalizes well known results when the boundaries are immobile. Furthermore, under certain conditions, if the boundary dynamics are strongly subdiffusive, we show the appearance of an interesting non-monotonicity in the time dependence of the MSD, giving rise to transient negative diffusion.