Interacting, running and tumbling: The active Dyson Brownian motion - Laboratoire de Physique Théorique et Hautes Energies Accéder directement au contenu
Article Dans Une Revue EPL - Europhysics Letters Année : 2023

Interacting, running and tumbling: The active Dyson Brownian motion

Résumé

Abstract We introduce and study a model in one dimension of N run-and-tumble particles (RTP) which repel each other logarithmically in the presence of an external quadratic potential. This is an “active” version of the well-known Dyson Brownian motion (DBM) where the particles are subjected to a telegraphic noise, with two possible states ± with velocity ± v 0 . We study analytically and numerically two different versions of this model. In model I a particle only interacts with particles in the same state, while in model II all the particles interact with each other. In the large time limit, both models converge to a steady state where the stationary density has a finite support. For finite N , the stationary density exhibits singularities, which disappear when . In that limit, for model I, using a Dean-Kawasaki approach, we show that the stationary density of + (respectively −) particles deviates from the DBM Wigner semi-circular shape, and vanishes with an exponent 3/2 at one of the edges. In model II, the Dean-Kawasaki approach fails but we obtain strong evidence that the density in the large N limit (still) retains a Wigner semi-circular shape.
Fichier principal
Vignette du fichier
2302.02937.pdf (2.43 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04535050 , version 1 (05-04-2024)

Identifiants

Citer

Léo Touzo, Pierre Le Doussal, Grégory Schehr. Interacting, running and tumbling: The active Dyson Brownian motion. EPL - Europhysics Letters, 2023, 142 (6), pp.61004. ⟨10.1209/0295-5075/acdabb⟩. ⟨hal-04535050⟩
24 Consultations
6 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More