We study the transport of self-propelled particles in dynamic complex environments. To obtain exact results, we introduce a model of Run-and-Tumble particles (RTPs) moving in discrete time on a $d$-dimensional cubic lattice in the presence of diffusing hard-core obstacles. We derive an explicit expression for the diffusivity of the RTP, which is exact in the limit of low density of fixed obstacles. To do so, we introduce a generalization of Kac's theorem on the mean return times of Markov processes, which we expect to be relevant for a large class of lattice gas problems. Our results show the diffusivity of RTPs to be non-monotonous in the tumbling probability for low enough obstacle mobility. These results prove the potential for optimization of the transport of RTPs in crowded and disordered environments with applications to motile artificial and biological systems.

中文翻译：

---

在拥挤的环境中优化运行颗粒的扩散

我们研究了动态复杂环境中自推进粒子的运输。为了获得准确的结果，我们引入了一个运行和滚动粒子（RTP）模型，该粒子在存在弥散性硬核障碍的情况下在$ d $维立方晶格上离散时间移动。我们为RTP的扩散性导出了一个明确的表达式，该表达式在固定障碍物的低密度限制内是精确的。为此，我们在马尔可夫过程的平均返回时间上引入了Kac定理的一般化，我们希望它与一大类晶格气体问题相关。我们的结果表明，RTP的扩散性在翻滚概率中具有足够低的障碍物移动性，因此是非单调的。