LAUSR

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 ∼tθ with θ=1/2 for α⩽1/2 , θ=α for 1/2 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 ∼tϕ where ϕ=1/2 for α⩽1 , ϕ=3/2−α for 13/2 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=12 for α⩽1 , and Δ=1−α2 for 1 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.