Harmonically trapped inertial run-and-tumble particle in one dimension

TL;DR

This paper analyzes the nonequilibrium stationary states of a one-dimensional inertial run-and-tumble particle in a harmonic trap, revealing how inertia influences phase space confinement and distribution transitions under varying activity and damping conditions.

Contribution

It provides an analytical characterization of phase space confinement and distribution transitions for inertial active particles in harmonic traps, highlighting the effects of inertia and activity regimes.

Findings

Inertia causes phase space confinement in specific regions.

Distribution transitions depend on activity and damping regimes.

Distinct behaviors in overdamped and underdamped cases.

Abstract

We study the nonequilibrium stationary state of a one-dimensional inertial run-and-tumble particle (IRTP) trapped in a harmonic potential. We find that the presence of inertia leads to two distinct dynamical scenarios, namely, overdamped and underdamped, characterized by the relative strength of the viscous and the trap time-scales. We also find that inertial nature of the active dynamics leads to the particle being confined in specific regions of the phase plane in the overdamped and underdamped cases, which we compute analytically. Moreover, the interplay of the inertial and active time-scales gives rise to several sub-regimes, which are characterized by very different behaviour of position and velocity fluctuations of the IRTP. In particular, in the underdamped regime, both the position and velocity undergoes transitions from a novel multi-peaked structure in the strongly active limit to a single peaked Gaussian-like distribution in the passive limit. On the other hand, in the overdamped scenario, the position distribution shows a transition from a U-shape to a dome-shape, as activity is decreased. Interestingly, the velocity distribution in the overdamped scenario shows two transitions -- from a single-peaked shape with an algebraic divergence at the origin in the strongly active regime to a double peaked one in the moderately active regime to a dome-shaped one in the passive regime.