{
  "id": "1906.11280",
  "version": "v1",
  "published": "2019-06-26T18:13:30.000Z",
  "updated": "2019-06-26T18:13:30.000Z",
  "title": "Time evolution of correlation functions in quantum many-body systems",
  "authors": [
    "Álvaro M. Alhambra",
    "Jonathon Riddell",
    "Luis Pedro García-Pintos"
  ],
  "comment": "5+10 pages, 4 figures, comments welcome",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "cond-mat.str-el"
  ],
  "abstract": "We give rigorous analytical results on the temporal behavior of two-point correlation functions -- also known as dynamical response functions or Green's functions -- in closed many-body quantum systems. We show that in a large class of models the correlation functions factorize at late times $\\langle A(t) B\\rangle_\\beta \\rightarrow \\langle A \\rangle_\\beta \\langle B \\rangle_\\beta$, thus proving that dissipation emerges out of the unitary dynamics of the system. We also show that the fluctuations around this late-time value are bounded by the purity of the thermal ensemble, which generally decays exponentially with system size. For auto-correlation functions we provide an upper bound on the timescale at which they reach the factorized late time value. Remarkably, this bound is only a function of local expectation values, and does not increase with system size. We give numerical examples that show that this bound is a good estimate in non-integrable models, and argue that the timescale that appears can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to further classes of two-point functions such as the symmetrized ones and the Kubo function that appears in linear response theory, for which we give analogous results.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-26T18:13:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum many-body systems",
      "time evolution",
      "factorized late time value",
      "closed many-body quantum systems",
      "two-point correlation functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}