Totally asymmetric simple exclusion process with resetting

We study the one-dimensional totally asymmetric simple exclusion process (TASEP) with open boundaries having the additional dynamical feature of stochastic resetting to the initial, empty state. The system evolves according to the TASEP dynamics with particles entering the input side with rate beta and leaving the other side with rate beta. The system is brought back to its initial state of an empty lattice at random intervals tau. These intervals are drawn from probability distributions, for which we consider two possibilities-a power law similar to tau(-(1+gamma)) with gamma > 0, and an exponential distribution lambda e(-lambda tau). We use approximate expressions for the time evolution of density on the lattice for a normal TASEP to calculate the reset- averaged density as a function of time. We find that in the limit of large time, the system achieves a steady state when gamma > 1, while for gamma < 1 we see a time-dependent scaling function. The large time behaviour of the density distribution shows a power law decay at the input boundary in all the phases while it shows a non-monotonic behaviour in the high-density phase of the TASEP. One sees this monotonic behaviour also for the exponential resetting, with the system always achieving a steady state in the limit of long times. We also perform numerical simulations, results from which show good agreement with our analytic expressions.