Ramifications of disorder on active particles in one dimension

Abstract

The effects of quenched disorder on a single and many active run-and-tumble particles are studied in one dimension. For a single particle, we consider both the steady-state distribution and the particle's dynamics subject to disorder in three parameters: a bounded external potential, the particle's speed, and its tumbling rate. We show that in the case of a disordered potential, the behavior is like an equilibrium particle diffusing on a random force landscape, implying a dynamics that is logarithmically slow in time. In the situations of disorder in the speed or tumbling rate, we find that the particle generically exhibits diffusive motion, although particular choices of the disorder may lead to anomalous diffusion. Based on the single-particle results, we find that in a system with many interacting particles, disorder in the potential leads to strong clustering. We characterize the clustering in two different regimes depending on the system size and show that the mean cluster size scales with the system size, in contrast to nondisordered systems.

Current fluctuations in non-interacting run-and-tumble particles in one-dimension

“…Even at the single-particle level, RTP displays interesting behaviour and several single-particle observables have been studied recently. These include the position distribution for a free RTP [12,14,21], non-Boltzmann stationary states for an RTP in a confining potential [19,[22][23][24][25], effects of disordered potentials [26], first-passage properties [27][28][29][30][31][32], the distribution of the time at which an RTP reaches its maximum displacement [33] and RTP subjected to stochastic resetting [34][35][36].…”

Trapping of a run-and-tumble particle in an inhomogeneous domain: the weak noise limit

“…The run-and-tumble model has also attracted considerable recent attention within the non-equilibrium statistical physics community, both at the single particle level and at the interacting population level, where it provides a simple example of active matter [12][13][14]. Studies at the single particle level include properties of the position density of a free RTP in one and higher dimensions [15][16][17][18], first-passage time (FPT) properties [19][20][21][22][23][24][25], RTPs under stochastic resetting [26][27][28], and non-Boltzmann stationary states for an RTP in a confining potential [29][30][31][32][33].…”

Occupation time of a run-and-tumble particle with resetting

“…The run-and-tumble model has also attracted considerable recent attention within the non-equilibrium statistical physics community, both at the single particle level and at the interacting population level, where it provides a simple example of active matter [19][20][21]. Studies at the single particle level include properties of the position density of a free RTP [22,23], non-Boltzmann stationary states for an RTP in a confining potential [24][25][26], first-passage time properties [27][28][29][30][31], and RTPs under stochastic resetting [32].…”