Dynamical metastability and re-entrant localization of trapped active elements with speed and orientation fluctuations

TL;DR

This paper provides an exact analytical study of active particles in harmonic traps, revealing complex dynamical behaviors including metastability, re-entrant localization, and non-Gaussian steady states driven by speed and orientation fluctuations.

Contribution

It introduces an exact Fokker-Planck based method to analyze the dynamics of active particles with fluctuating speed, uncovering new metastable and re-entrant localization phenomena.

Findings

Identification of intermediate metastable saturation in mean-squared displacement.

Discovery of bimodal and heavy-tailed non-Gaussian steady-state distributions.

Mapping of phase diagrams showing Gaussian and non-Gaussian regimes with re-entrant transitions.

Abstract

We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a $d$-dimensional harmonic trap, modeling active speed generation through an Ornstein-Uhlenbeck process. Our approach employs an exact analytic method based on the Fokker-Planck equation to compute time-dependent moments of any dynamical variable of interest across arbitrary dimensions. We analyze dynamical crossovers in particle displacement before reaching the steady state, focusing on three key timescales: speed relaxation, persistence, and dynamical relaxation in the trap. Notably, for slow active speed relaxation, we observe an intermediate time metastable saturation in the mean-squared displacement before reaching the final steady state. The steady-state distributions of particle positions exhibit two types of non-Gaussian departures based on control parameters: bimodal distributions with negative excess kurtosis and heavy-tailed unimodal distributions with positive excess kurtosis. We obtain detailed steady-state phase diagrams using the exact calculation of excess kurtosis, identifying Gaussian and non-Gaussian regions and possible re-entrant transitions.