{
  "id": "1908.02263",
  "version": "v1",
  "published": "2019-08-06T17:27:28.000Z",
  "updated": "2019-08-06T17:27:28.000Z",
  "title": "Hamiltonian Dynamics of a Sum of Interacting Random Matrices",
  "authors": [
    "Matteo Bellitti",
    "Siddhardh Morampudi",
    "Chris R. Laumann"
  ],
  "categories": [
    "cond-mat.stat-mech",
    "hep-th",
    "quant-ph"
  ],
  "abstract": "In ergodic quantum systems, physical observables have a non-relaxing component if they \"overlap\" with a conserved quantity. In interacting microscopic models, how to isolate the non-relaxing component is unclear. We compute exact dynamical correlators governed by a Hamiltonian composed of two large interacting random matrices, $H=A+B$. We analytically obtain the late-time value of $\\langle A(t) A(0) \\rangle$; this quantifies the non-relaxing part of the observable $A$. The relaxation to this value is governed by a power-law determined by the spectrum of the Hamiltonian $H$, independent of the observable $A$. For Gaussian matrices, we further compute out-of-time-ordered-correlators (OTOCs) and find that the existence of a non-relaxing part of $A$ leads to modifications of the late time values and exponents. Our results follow from exact resummation of a diagrammatic expansion and hyperoperator techniques.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-06T17:27:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hamiltonian dynamics",
      "late time values",
      "non-relaxing component",
      "large interacting random matrices",
      "non-relaxing part"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}