Exact solution of a boundary tumbling particle system in one dimension

2022/06/13 by Connor Roberts, Gunnar Pruessner, Roberts, Connor +1 · 2 citations
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2206.06105

openalex publication_date 2022/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We derive the fully time-dependent solution to a run-and-tumble model for a particle which has tumbling restricted to the boundaries of a one-dimensional interval. This is achieved through a field-theoretic perturbative framework by exploiting an elegant underlying structure of the perturbation theory. We calculate the particle densities, currents and variance as well as characteristics of the boundary tumbling. The analytical findings, in agreement with Monte-Carlo simulations, show how the particle densities are linked to the scale of diffusive fluctuations at the boundaries. The generality of our approach suggests it could be readily applied to similar problems described by Fokker-Planck equations containing localised reaction terms.

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