Symmetric Exclusion Process under Power-law Stochastic Resetting

Abstract

We study the behaviour of the Symmetric Exclusion Process in the presence of a non- Markovian stochastic resetting, where the system’s configuration is reset to a step-like profile at power-law waiting times with an exponent α. We find that power-law resetting leads to a rich behaviour for the diffusive and total currents, as well as the density profile. For α < 1, we show that, in the limit of large system size L → ∞, the density profile eventually becomes uniform while the average diffusive current grows sub-linearly with time t, with an exponent that lies between 1/2 and 1. For any finite L, however, the current grows ∼ t^α at late-times t ≫ L2. We develop a perturbative approach to get the distributions of the diffusive current and explain the origins of certain peculiar ‘peaks’ in them. Furthermore, we find that the average total current grows ∼√t. Using a renewal approach, we also compute the total current distributions, which turn out to be strongly non-Gaussian and bimodal for α ≃ 1/2. For α > 1, the system relaxes to an eventual non-trivial stationary density profile, which we compute exactly. In this regime, the average diffusive current grows ∼ t. The total current, on the other hand, reaches a stationary distribution with typical non-Gaussian fluctuations and a diverging average for α ≤ 3/2, while for α > 3/2 the average total current reaches a stationary value.