{
  "id": "2209.11256",
  "version": "v1",
  "published": "2022-09-22T18:03:06.000Z",
  "updated": "2022-09-22T18:03:06.000Z",
  "title": "Self-Similarity Among Energy Eigenstates",
  "authors": [
    "Zhelun Zhang",
    "Zhenduo Wang",
    "Biao Wu"
  ],
  "comment": "14 pages, 14 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "In a quantum system, different energy eigenstates have different properties or features, allowing us define a classifier to divide them into different groups. We find that the ratio of each type of energy eigenstates in an energy shell $[E_{c}-\\Delta E/2,E_{c}+\\Delta E/2]$ is invariant with changing width $\\Delta E$ or Planck constant $\\hbar$ as long as the number of eigenstates in the shell is statistically large enough. We give an argument that such self-similarity in energy eigenstates is a general feature for all quantum systems, which is further illustrated numerically with various quantum systems, including circular billiard, double top model, kicked rotor, and Heisenberg XXZ model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-22T18:03:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "energy eigenstates",
      "quantum system",
      "self-similarity",
      "heisenberg xxz model",
      "circular billiard"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}