Saved in:
Bibliographic Details
Main Authors: Romano, Jacopo, Gambassi, Andrea
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2508.20756
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908508342976512
author Romano, Jacopo
Gambassi, Andrea
author_facet Romano, Jacopo
Gambassi, Andrea
contents We study the stochastic dynamics of a symmetric self-chemotactic particle and determine the long-time behavior of its mean squared displacement (MSD). The attractive or repulsive interaction of the particle with the chemical field that it generates induces a non-linear, non-Markovian effective dynamics, which results into anomalous diffusion for spatial dimensions $d \leq 2$. In one spatial dimension, we map the case of repulsive chemotaxis onto a run-and-tumble-like dynamics, leading to an MSD which, as a function of the elapsed time $t$, grows superdiffusively with exponent $4/3$. In the presence of attractive chemotaxis, instead, the particle exhibits a slowdown, with the MSD growing logarithmically with time. In $d=2$, we find logarithmic aging of the diffusion coefficient, while in $d=3$ the motion reverts standard diffusive behavior with a renormalized diffusion coefficient.
format Preprint
id arxiv_https___arxiv_org_abs_2508_20756
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Anomalous diffusion and run-and-tumble motion of a chemotactic particle in low dimensions
Romano, Jacopo
Gambassi, Andrea
Statistical Mechanics
We study the stochastic dynamics of a symmetric self-chemotactic particle and determine the long-time behavior of its mean squared displacement (MSD). The attractive or repulsive interaction of the particle with the chemical field that it generates induces a non-linear, non-Markovian effective dynamics, which results into anomalous diffusion for spatial dimensions $d \leq 2$. In one spatial dimension, we map the case of repulsive chemotaxis onto a run-and-tumble-like dynamics, leading to an MSD which, as a function of the elapsed time $t$, grows superdiffusively with exponent $4/3$. In the presence of attractive chemotaxis, instead, the particle exhibits a slowdown, with the MSD growing logarithmically with time. In $d=2$, we find logarithmic aging of the diffusion coefficient, while in $d=3$ the motion reverts standard diffusive behavior with a renormalized diffusion coefficient.
title Anomalous diffusion and run-and-tumble motion of a chemotactic particle in low dimensions
topic Statistical Mechanics
url https://arxiv.org/abs/2508.20756