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Exact position distribution of a harmonically confined run-and-tumble particle in two dimensions.
- Source :
-
Physical review. E [Phys Rev E] 2022 Nov; Vol. 106 (5-1), pp. 054133. - Publication Year :
- 2022
-
Abstract
- We consider an overdamped run-and-tumble particle in two dimensions, with self-propulsion in an orientation that stochastically rotates by 90^{∘} at a constant rate, clockwise or counterclockwise with equal probabilities. In addition, the particle is confined by an external harmonic potential of stiffness μ, and possibly diffuses. We find the exact time-dependent distribution P(x,y,t) of the particle's position, and in particular, the steady-state distribution P_{st}(x,y) that is reached in the long-time limit. We also find P(x,y,t) for a "free" particle, μ=0. We achieve this by showing that, under a proper change of coordinates, the problem decomposes into two statistically independent one-dimensional problems, whose exact solution has recently been obtained. We then extend these results in several directions, to two such run-and-tumble particles with a harmonic interaction, to analogous systems of dimension three or higher, and by allowing stochastic resetting.
Details
- Language :
- English
- ISSN :
- 2470-0053
- Volume :
- 106
- Issue :
- 5-1
- Database :
- MEDLINE
- Journal :
- Physical review. E
- Publication Type :
- Academic Journal
- Accession number :
- 36559430
- Full Text :
- https://doi.org/10.1103/PhysRevE.106.054133