Run-and-tumble particle in one-dimensional confining potential: Steady state, relaxation and first passage properties

Abstract

We study the dynamics of a one-dimensional run and tumble particle subjected to confining potentials of the type $V(x)=\alpha |x{|}^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$ values. We show that the stationary probability density $P(x)$ has a rich behavior in the $(p,\alpha )$-plane. For $p>1$, the distribution has a finite support in $[x_{-},x_{+}]$ and there is a critical line ${\alpha }_c(p)$ that separates an active-like phase for $\alpha >{\alpha }_c(p)$ where $P(x)$ diverges at $x_{\pm }$, from a passive-like phase for $\alpha <{\alpha }_c(p)$ where $P(x)$ vanishes at $x_{\pm }$. For $p<1$, the stationary density $P(x)$ collapses to a delta function at the origin, $P(x)=\delta (x)$. In the marginal case $p=1$, we show that, for $\alpha <{\alpha }_c$, the stationary density $P(x)$ is a symmetric exponential, while for $\alpha >{\alpha }_c$, it again is a delta function $P(x)=\delta (x)$. For the special cases $p=2$ and $p=1$, we obtain exactly the full time-dependent distribution $P(x,t)$, that allows us to study how the system relaxes to its stationary state. In addition, in these two cases, we also study analytically the full distribution of the first-passage time to the origin. Numerical simulations are in complete agreement with our analytical predictions.

arXiv comment15 pages, 12 figures. Published version

References in corpus (15)

• Active Particles in Complex and Crowded Environments
• The Mechanics and Statistics of Active Matter
• Motility-Induced Phase Separation
• How far from equilibrium is active matter?
• Persistence and First-Passage Properties in Non-equilibrium Systems
• Pressure is not a state function for generic active fluids
• The statistical physics of active matter: from self-catalytic colloids to living cells
• Run and tumble particle under resetting: a renewal approach
• Steady state, relaxation and first-passage properties of a run-and-tumble particle in one-dimension
• Dynamics of a self-propelled particle in a harmonic trap
• Persistence in Nonequilibrium Systems
• Active Brownian Motion in Two Dimensions
• Stationary superstatistics distributions of trapped run-and-tumble particles
• Active processes in one dimension
• Duality Between Relaxation and First Passage in Reversible Markov Dynamics: Rugged Energy Landscapes Disentangled

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