Hard core run and tumble particles on a one dimensional lattice

TL;DR

This paper investigates the large-scale behavior of one-dimensional run and tumble particles with persistent motion, mapping the system to a mass transfer model, and analyzing steady states and hydrodynamic properties.

Contribution

It introduces a mapping of run and tumble particles to a mass transfer model and computes steady state distributions and hydrodynamic coefficients, revealing Einstein relation violations.

Findings

Steady state single site mass distribution derived for different spin-flip rates.

Hydrodynamic coefficients of diffusivity and conductivity calculated for both regimes.

Demonstration of Einstein relation violation in the system.

Abstract

We study the large scale behavior of a collection of hard core run and tumble particles on a one dimensional lattice with periodic boundary conditions. Each particle has persistent motion in one direction decided by an associated spin variable until the direction of spin is reversed. We map the run and tumble model to a mass transfer model with fluctuating directed bonds. We calculate the steady state single site mass distribution in the mass model within a mean field approximation for larger spin-flip rates and by analyzing an appropriate coalescence fragmentation model for small spin-flip rates. We also calculate the hydrodynamic coefficients of diffusivity and conductivity for both large and small spin-flip rates and show that the Einstein relation is violated in both regimes. We also show how the non-gradient nature of the process can be taken into account in a systematic manner to calculate the hydrodynamic coefficients.