{
  "id": "quant-ph/0410099",
  "version": "v2",
  "published": "2004-10-13T14:50:57.000Z",
  "updated": "2005-03-17T10:17:11.000Z",
  "title": "Mesoscopic Fluctuations of the Loschmidt Echo",
  "authors": [
    "Cyril Petitjean",
    "Philippe Jacquod"
  ],
  "comment": "Final, extended version; to appear in Physical Review E",
  "journal": "Phys. Rev. E 71, 036223 (2005)",
  "doi": "10.1103/PhysRevE.71.036223",
  "categories": [
    "quant-ph",
    "cond-mat.mes-hall",
    "nlin.CD"
  ],
  "abstract": "We investigate the time-dependent variance of the fidelity with which an initial narrow wavepacket is reconstructed after its dynamics is time-reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time $t_c$, after which it decays. To leading order in the effective Planck's constant $\\hbar_{\\rm eff}$, this decay is given by the sum of a classical term $\\simeq \\exp[-2 \\lambda t]$, a quantum term $\\simeq 2 \\hbar_{\\rm eff} \\exp[-\\Gamma t]$ and a mixed term $\\simeq 2 \\exp[-(\\Gamma+\\lambda)t]$. Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent $\\lambda$ in a larger parameter range. Our results are confirmed by numerical simulations.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-03-17T10:17:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "loschmidt echo",
      "mesoscopic fluctuations",
      "initial narrow wavepacket",
      "variance first rises",
      "larger parameter range"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "APS",
      "journal": "Phys. Rev. E"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}