Symmetric exclusion process under stochastic power-law resetting

Abstract

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 ∼ t θ with θ = 1 / 2 for α ⩽ 1 / 2 , θ = α for 1 / 2 < α ⩽ 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 ∼ t ϕ where ϕ = 1 / 2 for α ⩽ 1 , ϕ = 3 / 2 − α for 1 < α ⩽ 3 / 2 , while for α > 3 / 2 the average total current reaches a stationary value, which we compute exactly. The standard deviation of the total current also shows an algebraic growth with an exponent Δ = 1 2 for α ⩽ 1 , and Δ = 1 − α 2 for 1 < α ⩽ 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.