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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.20756 |
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| _version_ | 1866908508342976512 |
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| 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 |