Field Theory of Active Brownian Particles with Dry Friction

TL;DR

This paper develops a field theoretic framework to analyze the motion of active Brownian particles with dry friction, providing analytical and numerical insights into their diffusion behavior in one- and two-dimensional systems.

Contribution

It introduces a novel field theoretic approach for active particles with dry friction, extending existing models and enabling analytical calculation of diffusion coefficients.

Findings

Derived analytical expressions for diffusion coefficients with dry friction.

Validated theoretical results with numerical simulations.

Provided a method to estimate dry friction coefficients experimentally.

Abstract

We present a field theoretic approach to capture the motion of a particle with dry friction for one- and two-dimensional diffusive particles, and further expand the framework for two-dimensional active Brownian particles. Starting with the Fokker-Planck equation and introducing the Hermite polynomials as the corresponding eigen-functions, we obtain the actions and propagators. Using a perturbation expansion, we calculate the effective diffusion coefficient in the presence of both wet and dry frictions in a perturbative way via the Green-Kubo relation. We further compare the analytical result with the numerical simulation. Our result can be used to estimate the values of dry friction coefficient in experiments.