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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 FokkerPlanck 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 potential re-entrant transitions.
