Abstract

Zoom link: https://maths-cam-ac-uk.zoom.us/j/94018037756

We will discuss a general framework to study the distribution of the flux through the origin up to time t, in a non-interacting one-dimensional system of particles with a step initial condition with a fixed density of particles to the left of the origin. We will focus principally on two cases: (i) when the particles undergo diffusive dynamics (passive case) and (ii) run-and-tumble dynamics for each particle (active case). In analogy with disordered systems, we will consider the flux distribution both for the annealed and the quenched initial conditions, for the passive and active particles. In the annealed case, we will show that, for arbitrary particle dynamics, the flux distribution is a Poissonian with a mean that can be computed exactly in terms of the Green’s function of the single particle dynamics. For the quenched case, we will show that, for the run-and-tumble dynamics, the quenched flux distribution takes an anomalous large deviation form at large times with a non-trivial large deviation function.