标题： 趋化粒子在低维空间中的异常扩散和跑动-停顿运动 显示英文标题

标题： Anomalous diffusion and run-and-tumble motion of a chemotactic particle in low dimensions

摘要： 我们研究对称自趋化粒子的随机动力学，并确定其均方位移（MSD）的长时间行为。 该粒子与它生成的化学场之间的吸引或排斥相互作用导致了非线性、非马尔可夫的有效动力学，这在空间维度$d \leq 2$时导致异常扩散。 在一维空间中，我们将排斥趋化的情况映射到类似跑-停的动力学，导致 MSD 随时间$t$的增长呈现超扩散性，指数为$4/3$。 而在吸引趋化存在的情况下，粒子表现出减速，MSD 随时间呈对数增长。 在$d=2$中，我们发现扩散系数的对数老化现象，而在$d=3$中，运动恢复为具有重整化扩散系数的标准扩散行为。 显示英文摘要

摘要： 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.