Dresden 2026 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 49: Active Matter V (joint session DY/BP)
DY 49.7: Vortrag
Donnerstag, 12. März 2026, 11:30–11:45, ZEU/0160
Exact Stationary State of a d-dimensional Run-and-Tumble Particle in a Harmonic Potential — •Mathis Guéneau1, Grégory Schehr2, and Satya N. Majumdar3 — 1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany — 2Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France — 3LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France
We study the stationary state of a run-and-tumble particle (RTP) confined in a harmonic potential in arbitrary dimension d. Owing to isotropy, all statistical properties of the steady state are fully encoded in the distribution of a single coordinate. This coordinate follows an effective one-dimensional dynamics with a piecewise-constant self-propulsion velocity drawn from a prescribed distribution. We obtain the exact stationary distribution by identifying a stick-breaking process and a Dirichlet process in the dynamics, and by using known results for these processes. This framework allows us to compute exactly the full radial distribution, the joint law of the coordinates, and their moments, and to extend these results to include thermal noise. We further characterize the shape transition of the stationary state, from active-like to passive-like behavior, and show that it can be analyzed for arbitrary external potentials.
Keywords: Run-and-Tumble Particles; Stochastic Processes; Non Equilibirum Steady State; Stick-Breaking Processes