Symmetric Exclusion Process under Stochastic Power-law Resetting

Abstract

We study the behaviour of a symmetric exclusion process in the presence of non-Markovian stochastic resetting, where the configuration of the system is reset to a step-like profile at power-law waiting times with an exponent $α$. We find that the power-law resetting leads to a rich behaviour for the currents, as well as density profile. We show that, for any finite system, for $α<1$, the density profile eventually becomes uniform while for $α>1$, an eventual non-trivial stationary profile is reached. We also find that, in the limit of thermodynamic system size, at late times, the average diffusive current grows $\sim t^θ$ with $θ= 1/2$ for $α\le 1/2$, $θ= α$ for $1/2 < α\le 1$ and $θ=1$ for $α> 1$. We also analytically characterize the distribution of the diffusive current in the short-time regime using a trajectory-based perturbative approach. Using numerical simulations, we show that in the long-time regime, the diffusive current distribution follows a scaling form with an $α-$dependent scaling function. We also characterise the behaviour of the total current using renewal approach. We find that the average total current also grows algebraically $\sim t^ϕ$ where $ϕ= 1/2$ for $α\le 1$, $ϕ=3/2-α$ for $1 < α\le 3/2$, while for $α> 3/2$ the average total current reaches a stationary value, which we compute exactly. The variance of the total current also shows an algebraic growth with an exponent $Δ=1$ for $α\le 1$, and $Δ=2-α$ for $1 < α\le 2$, whereas it approaches a constant value for $α>2$. The total current distribution remains non-stationary for $α<1$, while, for $α>1$, it reaches a non-trivial and strongly non-Gaussian stationary distribution, which we also compute using the renewal approach.