Symmetric exclusion process under stochastic resetting

Abstract

We study the behaviour of a Symmetric Exclusion Process (SEP) in presence of stochastic resetting where the configuration of the system is reset to a step-like profile with a fixed rate r. We show that the presence of resetting affects both the stationary and dynamical properties of SEP strongly. We compute the exact time-dependent density profile and show that the stationary state is characterized by a non-trivial inhomogeneous profile in contrast to the flat one for r = 0. We also show that for r > 0 the average diffusive current grows linearly with time t, in stark contrast to the √ t growth for r = 0. In addition to the underlying diffusive current, we also identify the resetting current in the system which emerges due to the sudden relocation of the particles to the step-like configuration. We compute the probability distributions of the diffusive current and the total current (comprising of the diffusive and the resetting current) using the renewal approach. We demonstrate that while the typical fluctuations of the diffusive current around the mean are typically Gaussian, the distribution of the total current shows a strong non-Gaussian behaviour. arXiv:1906.11801v1 [cond-mat.stat-mech]

Non-conserving zero-range processes with extensive rates under resetting

“…The hopping process can be mapped to a set of independent random walkers on a fully connected, large set of states. Recent developments on stochastic resetting of interacting particle systems have addressed properties of the symmetric exclusion process [36] and totally asymmetric exclusion process [42], and in [43], the phase diagram in the plane of temperature and resetting rate has been presented for the Ising model, an interacting system with a thermodynamic phase transition in its equilibrium state. However, the present model allows for a mapping of the model of growing networks, as well as to a microscopic version of Kingman's house-of-cards model.…”

Time-dependent density of diffusion with stochastic resetting is invariant to return speed

“…(23) from the result in Eq. (21). An exact, real-time, formula can also be given for the probability to be in the return phase p R (t); and hence for the probability p D (t) = 1 − p R (t) to be in the diffusive phase.…”

“…The simple model of diffusion with stochastic resetting has been extended and generalized to cover: diffusion in the presence of a potential [6][7][8], in a domain [9][10][11][12], and arbitrary dimensions [13]; diffusion in the presence of non-exponential resetting time distributions e.g., deterministic [14], intermittent [4], non-Markovian [15], non-stationary [16], with general time dependent resetting rates [17], as well as other protocols [18]; and diffusion in the presence of interactions [19][20][21]. The effect of resetting on random walks [22,23], continuous time random walks [24][25][26], Lévy flights [27,28], and other forms of stochastic motion [29][30][31][32][33], has also been studied.…”

Invariants of motion with stochastic resetting and space-time coupled returns

“…Noteworthy in this regard is the Evans-Majumdar model for diffusion with stochastic resetting [2,3]. This model has led to a large volume of work covering diffusion with resetting in the presence of a potential field [5,37,38], in different geometrical confinements [39][40][41][42], in higher dimensions [43], with non-Poissonian resetting protocols [44][45][46][47][48], with interactions [49][50][51], and more. The model was further extended to study other, i.e.…”