{
  "id": "2004.03501",
  "version": "v1",
  "published": "2020-04-07T15:53:57.000Z",
  "updated": "2020-04-07T15:53:57.000Z",
  "title": "Quantum Chaos on Complexity Geometry",
  "authors": [
    "Bin Yan",
    "Wissam Chemissany"
  ],
  "comment": "5 pages, 1 figure",
  "categories": [
    "quant-ph",
    "cond-mat.stat-mech",
    "hep-th"
  ],
  "abstract": "This article tackles a fundamental long-standing problem in quantum chaos, namely, whether quantum chaotic systems can exhibit sensitivity to initial conditions, in a form that directly generalizes the notion of classical chaos in phase space. We develop a linear response theory for complexity, and demonstrate that the complexity can exhibit exponential sensitivity in response to perturbations of initial conditions for chaotic systems. Two immediate significant results follows: i) the complexity linear response matrix gives rise to a spectrum that fully recovers the Lyapunov exponents in the classical limit, and ii) the linear response of complexity is given by the out-of-time order correlators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-07T15:53:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum chaos",
      "complexity geometry",
      "initial conditions",
      "complexity linear response matrix",
      "out-of-time order correlators"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}