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We present exact results for the fluctuations in the number of particlescrossing the origin up to time $t$ in a collection of non-interacting run andtumble particles in one dimension. In contrast to passive systems, such activeparticles are endowed with two inherent degrees of freedom: positions andvelocities, which can be used to construct density and magnetization fields. Weintroduce generalized disorder averages associated with both these fields andperform annealed and quenched averages over various initial conditions. We showthat the variance $\sigma^2$ of the current in annealed versus quenchedmagnetization 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 inthe strictly quenched scenario, where both the density and magnetization fieldsare initially frozen, the fluctuations in the current are strongly suppressed.Importantly, these anomalous fluctuations cannot be obtained solely by freezingthe density field.

Generalized disorder averages and current fluctuations in run and tumble particles