{
  "id": "2206.00704",
  "version": "v1",
  "published": "2022-06-01T18:35:21.000Z",
  "updated": "2022-06-01T18:35:21.000Z",
  "title": "Emergence of Fermi's Golden Rule",
  "authors": [
    "Tobias Micklitz",
    "Alan Morningstar",
    "Alexander Altland",
    "David A. Huse"
  ],
  "comment": "4 pages, 2 figures, supplementary material",
  "categories": [
    "quant-ph",
    "cond-mat.mes-hall"
  ],
  "abstract": "Fermi's Golden Rule (FGR) applies in the limit where an initial quantum state is weakly coupled to a {\\it continuum} of other final states overlapping its energy. Here we investigate what happens away from this limit, where the set of final states is discrete, with a nonzero mean level spacing; this question arises in a number of recently investigated many-body systems. For different symmetry classes, we analytically and/or numerically calculate the universal crossovers in the average decay of the initial state as the level spacing is varied, with the Golden Rule emerging in the limit of a continuum. Among the corrections to the exponential decay of the initial state given by FGR is the appearance of the spectral form factor in the long-time regime for small but nonzero level spacing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-01T18:35:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fermis golden rule",
      "final states",
      "initial state",
      "spectral form factor",
      "initial quantum state"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}