In this work, we obtain a third-order linear differential equation for stationary distributions of run-and-tumble particles in two dimensions in a harmonic trap. The equation represents the condition $j=0$, where $j$ is a flux. Since an analogous equation for passive Brownian particles is first-order, a second- and third-order term are features of active motion. In all cases, the solution has a form of a convolution of two distributions: the Gaussian distribution representing the Boltzmann distribution of passive particles, and the beta distribution representing active motion at zero temperature.

• Received 29 May 2022
• Accepted 1 August 2022

DOI:https://doi.org/10.1103/PhysRevE.106.024121

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society