Exact moments for trapped active particles: inertial impact on steady-state properties and re-entrance

TL;DR

This paper derives exact moments for inertial active Brownian particles in harmonic traps, revealing how inertia influences steady-state properties and re-entrance phenomena through a Laplace transform approach.

Contribution

It provides explicit formulas for dynamical moments of inertial active particles in traps, highlighting the impact of inertia on steady-state behavior and phase re-entrance.

Findings

Effective diffusivity depends on inertia and trap strength.

Steady-state kinetic temperature varies with inertia.

Re-entrance phenomena are demonstrated via phase diagrams.

Abstract

In this study, we investigate the behavior of inertial active Brownian particles in a $d$-dimensional harmonic trap in the presence of translational diffusion. While the solution of the Fokker-Planck equation is generally challenging, it can be utilized to compute the exact time evolution of all time-dependent dynamical moments using a Laplace transform approach. We present the explicit form for several moments of position and velocity in $d$-dimensions. An interplay of time scales assures that the effective diffusivity and steady-state kinetic temperature depend on both inertia and trap strength, unlike passive systems. We present detailed `phase diagrams' using kurtosis of velocity and position showing possibilities of re-entrance.