{
  "id": "2306.14825",
  "version": "v1",
  "published": "2023-06-26T16:33:14.000Z",
  "updated": "2023-06-26T16:33:14.000Z",
  "title": "Mesoscale mode coupling theory for the weakly asymmetric simple exclusion process",
  "authors": [
    "G. M. Schütz"
  ],
  "comment": "29 pages, 1 figure",
  "categories": [
    "cond-mat.stat-mech",
    "math.PR"
  ],
  "abstract": "The asymmetric simple exclusion process and its analysis by mode coupling theory (MCT) is reviewed. To treat the weakly asymmetric case at large space scale $x\\varepsilon^{-1}$, %(corresponding to small Fourier momentum at scale $p\\varepsilon$), large time scale $t \\varepsilon^{-\\chi}$ and weak hopping bias $b \\varepsilon^{\\kappa}$ in the limit $\\varepsilon \\to 0$ we develop a mesoscale MCT that allows for studying the crossover at $\\kappa=1/2$ and $\\chi=2$ from Kardar-Parisi-Zhang (KPZ) to Edwards-Wilkinson (EW) universality. The dynamical structure function is shown to satisfy for all $\\kappa$ an integral equation that is independent of the microscopic model parameters and has a solution that yields a scale-invariant function with the KPZ dynamical exponent $z=3/2$ at scale $\\chi=3/2+\\kappa$ for $0\\leq\\kappa<1/2$ and for $\\chi=2$ the exact Gaussian EW solution with $z=2$ for $\\kappa>1/2$. At the crossover point it is a function of both scaling variables which converges at macroscopic scale to the conventional MCT approximation of KPZ universality for $\\kappa<1/2$. This fluctuation pattern confirms long-standing conjectures for $\\kappa \\leq 1/2$ and is in agreement with mathematically rigorous results for $\\kappa>1/2$ despite the numerous uncontrolled approximations on which MCT is based.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-26T16:33:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "weakly asymmetric simple exclusion process",
      "mesoscale mode coupling theory",
      "pattern confirms long-standing conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}