Simple exclusion processes with local resetting

¹ Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino - Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
² INFN, Sezione di Torino - Via Pietro Giuria 1, I-10125 Torino, Italy
³ Consiglio Nazionale delle Ricerche - Istituto dei Sistemi Complessi (CNR-ISC) - Via dei Taurini 19, I-00185 Roma, Italy

^(a) alessandro.pelizzola@polito.it
^(b) marco.pretti@polito.it
^(c) marco.zamparo@polito.it

Received: 18 December 2020
Accepted: 4 March 2021

Abstract

We investigate the stationary state of symmetric and totally asymmetric simple exclusion processes with local resetting, on a one-dimensional lattice with periodic boundary conditions, using mean-field approximations, which appear to be exact in the thermodynamic limit, and kinetic Monte Carlo simulations. In both cases we find that in the thermodynamic limit the models exhibit three different regimes, depending on how the resetting rate scales with the system size. The totally asymmetric version of the model has a particularly rich behaviour, especially in an intermediate resetting regime where the resetting rate vanishes as the inverse of the system size, exhibiting 4 different phases, including phase separation.