{
  "id": "2205.07487",
  "version": "v1",
  "published": "2022-05-16T07:40:12.000Z",
  "updated": "2022-05-16T07:40:12.000Z",
  "title": "Trajectory phase transitions in non-interacting systems: all-to-all dynamics and the random energy model",
  "authors": [
    "Juan P. Garrahan",
    "Chokri Manai",
    "Simone Warzel"
  ],
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study the fluctuations of time-additive random observables in the stochastic dynamics of a system of $N$ non-interacting Ising spins. We mainly consider the case of all-to-all dynamics where transitions are possible between any two spin configurations with uniform rates. We show that the cumulant generating function of the time-integral of a normally distributed quenched random function of configurations, i.e., the energy function of the random energy model (REM), has a phase transition in the large $N$ limit for trajectories of any time extent. We prove this by determining the exact limit of the scaled cumulant generating function. This is accomplished by connecting the dynamical problem to a spectral analysis of the all-to-all quantum REM. We also discuss finite $N$ corrections as observed in numerical simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-16T07:40:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82C44",
      "60F10"
    ],
    "keywords": [
      "random energy model",
      "trajectory phase transitions",
      "all-to-all dynamics",
      "non-interacting systems",
      "distributed quenched random function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}