{
  "id": "1604.03380",
  "version": "v1",
  "published": "2016-04-12T12:48:55.000Z",
  "updated": "2016-04-12T12:48:55.000Z",
  "title": "Slowing down of so-called chaotic states: \"Freezing\" the initial state",
  "authors": [
    "Martin Belger",
    "Sarah De Nigris",
    "Xavier Leoncini"
  ],
  "comment": "Submitted to Discontinuity, Nonlinearity and Complexity. Special Issue for Valentin Afraimovich 70th birthday, Guest editor: Albert Luo",
  "categories": [
    "cond-mat.stat-mech",
    "nlin.CD"
  ],
  "abstract": "The so-called chaotic states that emerge on the model of $XY$ interacting on regular critical range networks are analyzed. Typical time scales are extracted from the time series analysis of the global magnetization. The large spectrum confirms the chaotic nature of the observable, anyhow different peaks in the spectrum allows for typical characteristic time-scales to emerge. We find that these time scales $\\tau(N)$ display a critical slowing down, i.e they diverge as $N\\rightarrow\\infty$. The scaling law is analyzed for different energy densities and the behavior $\\tau(N)\\sim\\sqrt{N}$ is exhibited. This behavior is furthermore explained analytically using the formalism of thermodynamic-equations of the motion and analyzing the eigenvalues of the adjacency matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-12T12:48:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "chaotic states",
      "initial state",
      "time series analysis",
      "regular critical range networks",
      "large spectrum confirms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}