Work

Run-and-tumble particles in a harmonic external field: Constructing the solution of the Fokker–Planck equation from the equations of motion

Year: 2026

Type: article

Abstract: A method for integrating the Langevin equations of motion for run-and-tumble particles is introduced to compute the joint distribution of their position and active velocity, with and without a harmonic external force field. The key step is the construction of the moments of the distribution and the correlation functions, conditional on the particles being in a specific state at the final time. For one-dimensional run-and-tumble particles in a harmonic external potential, the exact steady-state distributions for the tumble state, as well as for the run state conditional on a specified velocity direction, are obtained. This enables us to demonstrate their equivalence to the exact solutions of the corresponding Fokker-Planck equations.

Source: The Journal of Chemical Physics

DOI: 10.1063/5.0350332

Authors: Aoran Sun, Fangfu Ye, Jeff Z. Y. Chen

Institutions: Chinese Academy of Sciences, Institute of Physics, Wenzhou Institute, University of Chinese Academy of Sciences, University of Waterloo

Language: English

Topic: Micro and Nano Robotics

Subfield: Condensed Matter Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China

Awards: G3347919835, G5467704715