{
  "id": "2211.14120",
  "version": "v1",
  "published": "2022-11-25T14:03:03.000Z",
  "updated": "2022-11-25T14:03:03.000Z",
  "title": "Symmetric Exclusion Process under Stochastic Power-law Resetting",
  "authors": [
    "Seemant Mishra",
    "Urna Basu"
  ],
  "comment": "26 pages, 10 figures",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.soft"
  ],
  "abstract": "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 $\\alpha$. 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 $\\alpha<1$, the density profile eventually becomes uniform while for $\\alpha >1$, 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 $\\sim t^\\theta$ with $\\theta = 1/2$ for $\\alpha \\le 1/2$, $\\theta = \\alpha$ for $1/2 < \\alpha \\le 1$ and $\\theta=1$ for $\\alpha > 1$. 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 $\\alpha-$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 $\\sim t^{\\phi}$ where $\\phi = 1/2$ for $\\alpha \\le 1$, $\\phi=3/2-\\alpha$ for $1 < \\alpha \\le 3/2$, while for $\\alpha > 3/2$ the average total current reaches a stationary value, which we compute exactly. The variance of the total current also shows an algebraic growth with an exponent $\\Delta=1$ for $\\alpha \\le 1$, and $\\Delta=2-\\alpha$ for $1 < \\alpha \\le 2$, whereas it approaches a constant value for $\\alpha>2$. The total current distribution remains non-stationary for $\\alpha<1$, while, for $\\alpha>1$, it reaches a non-trivial and strongly non-Gaussian stationary distribution, which we also compute using the renewal approach.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-25T14:03:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric exclusion process",
      "stochastic power-law resetting",
      "average total current",
      "total current distribution remains non-stationary",
      "diffusive current"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}