Symmetric Exclusion Process under Stochastic Resetting

Urna Basu, Anupam Kundu, Arnab Pal

Published 2019-06-27Version 1

We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate $r.$ We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for $r=0.$ We also show that for $r>0$ the average diffusive current grows linearly with time $t,$ in stark contrast to the $\sqrt{t}$ growth for $r=0.$ In addition to the underlying diffusive current, we also identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration. We compute the probability distributions of the diffusive current and the total current (comprising of the diffusive and the resetting current) using the renewal approach. We demonstrate that while the typical fluctuations of the diffusive current around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour.