{
  "id": "2009.02249",
  "version": "v1",
  "published": "2020-09-04T15:29:00.000Z",
  "updated": "2020-09-04T15:29:00.000Z",
  "title": "Sensitivity of the spectral form factor to short-range level statistics",
  "authors": [
    "Wouter Buijsman",
    "Vadim Cheianov",
    "Vladimir Gritsev"
  ],
  "comment": "6 pages, 2 figures",
  "categories": [
    "cond-mat.dis-nn",
    "nlin.CD"
  ],
  "abstract": "The spectral form factor is a dynamical probe for level statistics of quantum systems. The early-time behaviour is commonly interpreted as a characterization of two-point correlations at large separation. We argue that this interpretation can be too restrictive by indicating that the self-correlation imposes a constraint on the spectral form factor integrated over time. More generally, we indicate that each expansion coefficient of the two-point correlation function imposes a constraint on the properly weighted time-integrated spectral form factor. We discuss how these constraints can affect the interpretation of the spectral form factor as a probe for ergodicity. We propose a new probe, which eliminates the effect of the constraint imposed by the self-correlation. The use of this probe is demonstrated for a model of randomly incomplete spectra and a Floquet model supporting many-body localization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-04T15:29:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "short-range level statistics",
      "time-integrated spectral form factor",
      "weighted time-integrated spectral form",
      "floquet model supporting many-body localization",
      "two-point correlation function imposes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}