Anomalous Diffusion and Run-and-Tumble Motion of a Chemotactic Particle in Low Dimensions
Abstract
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 nonlinear, non-Markovian effective dynamics, which results in anomalous diffusion for spatial dimensions d≤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 to standard diffusive behavior with a renormalized diffusion coefficient.
Fields of Study & Subjects
Mathematical Biology Tumor Growth
Micro and Nano Robotics
Spaceflight effects on biology
Publication details
- Journal / source
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Volume
- 136
- Issue
- 10
- Pages
- 107102–107102
- Publication date
- 28 January 2026
- Language
- EN