{
  "annotation_id": "36c42b69-817f-408a-955e-b9c1886ee342",
  "date_created": "2026-02-17T05:53:23.671000Z",
  "date_modified": "2026-02-17T05:53:23.671000Z",
  "file_hash": "7f0537cdc3d1d3d7fcb3dc183e3baa7a1be27d572af907152a5d626fcf6ef149",
  "private": false,
  "record": {
    "abstract": "The evolution of an isolated quantum system inevitably exhibits recurrence: the state returns to the vicinity of its initial condition after finite time. Despite its fundamental nature, a rigorous quantitative understanding of recurrence has been lacking. We establish upper bounds on the recurrence time, $t_{\\mathrm{rec}} \\lesssim t_{\\mathrm{exit}}(\\epsilon)(1/\\epsilon)^d$, where $d$ is the Hilbert-space dimension, $\\epsilon$ the neighborhood size, and $t_{\\mathrm{exit}}(\\epsilon)$ the escape time from this neighborhood. For pure states evolving under a Hamiltonian $H$, estimating $t_{\\mathrm{exit}}$ is equivalent to an inverse quantum speed limit problem: finding upper bounds on the time a time-evolved state $\\psi_t$ needs to depart from the $\\epsilon$-vicinity of the initial state $\\psi_0$. We provide a partial solution, showing that under mild assumptions $t_{\\mathrm{exit}}(\\epsilon) \\approx \\epsilon /\\sqrt{ \\Delta(H^2)}$, with $\\Delta(H^2)$ the Hamiltonian variance in $\\psi_0$. We show that our upper bound on $t_{\\mathrm{rec}}$ is generically saturated for random Hamiltonians. Finally, we analyze the impact of coherence of the initial state in the eigenbasis of $H$ on recurrence behavior.",
    "arxiv_id": "2601.10409",
    "authors": [
      "Marcin Kotowski",
      "Micha\u0142 Oszmaniec"
    ],
    "categories": [
      "quant-ph"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Tight bounds on recurrence time in closed quantum systems",
    "url": "https://arxiv.org/abs/2601.10409",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e9f8ae5b-0c64-43d5-8a06-0c02988c451b",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}