{
  "id": "2309.13126",
  "version": "v1",
  "published": "2023-09-22T18:22:56.000Z",
  "updated": "2023-09-22T18:22:56.000Z",
  "title": "Stretched-exponential relaxation in weakly-confined Brownian systems through large deviation theory",
  "authors": [
    "Lucianno Defaveri",
    "Eli Barkai",
    "David A. Kessler"
  ],
  "comment": "6 pages (12 with SM), 3 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Stretched-exponential relaxation is a widely observed phenomenon found in glassy systems. It was previously modeled with non-Markovian dynamics reflecting a memory effect. Here, we study a Brownian particle under the influence of a confining, albeit weak, potential field that grows with distance as a sub-linear power law. We find that for this memoryless model, observables display stretched-exponential relaxation. The probability density function of the system is studied using a rate function ansatz. We obtain analytically the stretched-exponential exponent along with an anomalous power-law scaling of length with time. The rate function exhibits a point of nonanalyticity, indicating a dynamical phase transition. In particular, the rate function is double-valued both to the left and right of this point, leading to four different rate functions, depending on the choice of initial conditions and symmetry.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-22T18:22:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation theory",
      "weakly-confined brownian systems",
      "observables display stretched-exponential relaxation",
      "rate function ansatz",
      "probability density function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}