2025/10/15 by Timothée Herbeau, Herbeau, Timothée, L. А. Pastur +5
Biochemistry, Genetics and Molecular Biology · #Diffusion and Search Dynamics #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2510.13589
openalex publication_date 2025/10/15 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28
We consider stochastic dynamics of a particle on a plane in presence of two noises and a confining parabolic potential - an analog of the experimentally-relevant Brownian Gyrator (BG) model. In contrast to the standard BG model, we suppose here that the time-evolution of the position components is driven not by Gaussian white-noises, but by two statistically-independent dichotomous noises. We calculate analytically the position variances and cross-correlations, as well as the mean angular momentum, which permits us to establish the conditions in which a spontaneous rotational motion of the particle around the origin takes place. We also present a numerical analysis of the mean angular velocity. Lastly, we calculate analytically some marginal position probability density functions revealing a remarkably rich behavior that emerges in such a system of two coupled linear stochastic differential equations. We show that depending on the values of parameters characterizing noises these distributions approach the steady-state forms defined on a finite support, having very unusual shapes, possessing multiple maxima and minima, plateaus and exhibiting a discontinuous behavior.