{
  "id": "2206.08739",
  "version": "v1",
  "published": "2022-06-17T12:52:50.000Z",
  "updated": "2022-06-17T12:52:50.000Z",
  "title": "Role of initial conditions in $1D$ diffusive systems: compressibility, hyperuniformity and long-term memory",
  "authors": [
    "Tirthankar Banerjee",
    "Robert L. Jack",
    "Michael E. Cates"
  ],
  "comment": "Main text: 6 pages, 2 figures; Supplemental Material: 9 pages, 1 figure",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density profile, and the mean-square displacement of tracers in homogeneous systems with single-file diffusion. For these two cases, we show analytically (via the propagator and Macroscopic Fluctuation Theory, respectively) that the long-term memory of initial conditions is mediated by a single static quantity: a generalized compressibility that quantifies the density fluctuations of the initial state. We thereby identify a universality class of hyperuniform initial states whose dynamical variances coincide with the `quenched' cases studied previously; we also describe a continuous family of other classes among which equilibrated (or `annealed') initial conditions are but one family member. We verify our predictions through extensive Monte Carlo simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-17T12:52:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial conditions",
      "long-term memory",
      "diffusive systems",
      "compressibility",
      "hyperuniformity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}