Active Brownian particle in harmonic trap: exact computation of moments, and re-entrant transition
arXiv:2005.14234 · doi:10.1088/1742-5468/abd031
Abstract
We consider an active Brownian particle in a -dimensional harmonic trap, in the presence of translational diffusion. While the Fokker-Planck equation can not in general be solved to obtain a closed form solution of the joint distribution of positions and orientations, as we show, it can be utilized to evaluate the exact time dependence of all moments, using a Laplace transform approach. We present explicit calculation of several such moments at arbitrary times and their evolution to the steady state. In particular we compute the kurtosis of the displacement, a quantity which clearly shows the difference of the active steady state properties from the equilibrium Gaussian form. We find that it increases with activity to asymptotic saturation, but varies non-monotonically with the trap-stiffness, thereby capturing a recently observed active- to- passive re-entrant behavior.
arXiv comment17 pages, 7 figures; version accepted for publication in Journal of Statistical Mechanics: Theory and Experiment
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