Generalized disorder averages and current fluctuations in run and tumble particles

TL;DR

This paper provides exact analytical results on current fluctuations in one-dimensional run and tumble particles, revealing how initial conditions and disorder averages influence fluctuation behavior over time.

Contribution

It introduces generalized disorder averages for active particles and uncovers novel short-time fluctuation differences between annealed and quenched initial states.

Findings

Variance scales linearly with time in annealed magnetization.

Variance scales quadratically with time in quenched magnetization.

Fluctuations are suppressed when both density and magnetization are initially frozen.

Abstract

We present exact results for the fluctuations in the number of particles crossing the origin up to time $t$ in a collection of non-interacting run and tumble particles in one dimension. In contrast to passive systems, such active particles are endowed with two inherent degrees of freedom: positions and velocities, which can be used to construct density and magnetization fields. We introduce generalized disorder averages associated with both these fields and perform annealed and quenched averages over various initial conditions. We show that the variance $\sigma^2$ of the current in annealed versus quenched magnetization situations exhibits a surprising difference at short times: $\sigma^2 \sim t$ versus $\sigma^2 \sim t^2$ respectively, with a $\sqrt{t}$ behavior emerging at large times. Our analytical results demonstrate that in the strictly quenched scenario, where both the density and magnetization fields are initially frozen, the fluctuations in the current are strongly suppressed. Importantly, these anomalous fluctuations cannot be obtained solely by freezing the density field.