PreprintCC BY-NC-SA 4.0arXiv
Run-and-tumble particles in a harmonic external field: constructing the solution of the Fokker-Planck equation from the equations of motion
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.
Versions
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BibTeX
@misc{sun2026runandtumble,
title = {{Run-and-tumble particles in a harmonic external field: constructing the solution of the Fokker-Planck equation from the equations of motion}},
author = {Aoran Sun and Fangfu Ye and Jeff Z. Y. Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24961},
eprint = {2610.24961},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24961},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Run-and-tumble particles in a harmonic external field: constructing the solution of the Fokker-Planck equation from the equations of motion
AU - Aoran Sun
AU - Fangfu Ye
AU - Jeff Z. Y. Chen
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.24961
UR - https://arxiv.org/abs/2610.24961
AB - 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.
ER -