{
  "annotation_id": "0682bc4e-be7c-4d93-901c-507eafe34a04",
  "date_created": "2026-03-02T18:01:39.323000Z",
  "date_modified": "2026-03-02T18:01:39.323000Z",
  "file_hash": "d1f14c193c552615d53c28ae917033733184484330e660dba7e0a1e768f1a798",
  "private": false,
  "record": {
    "abstract": "The buildup process of the probability density inside the quantum well of a\ndouble-barrier resonant structure is studied by considering the analytic\nsolution of the time dependent Schr\\\"{o}dinger equation with the initial\ncondition of a cutoff plane wave. For one level systems at resonance condition\nwe show that the buildup of the probability density obeys a simple charging up\nlaw, $| \\Psi (\\tau) / \\phi | =1-e^{-\\tau /\\tau_0},$ where $\\phi$ is the\nstationary wave function and the transient time constant $\\tau_0$ is exactly\ntwo lifetimes. We illustrate that the above formula holds both for symmetrical\nand asymmetrical potential profiles with typical parameters, and even for\nincidence at different resonance energies. Theoretical evidence of a crossover\nto non-exponential buildup is also discussed.",
    "arxiv_id": "quant-ph/0006052",
    "authors": [
      "Roberto Romo",
      "Jorge Villavicencio"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevB.60.R2142",
    "journal_ref": "Physical Review B Rapid Communications 60, R2142 (1999)",
    "title": "Dynamical description of the buildup process in resonant tunneling:   Evidence of exponential and non-exponential contributions",
    "url": "https://arxiv.org/abs/quant-ph/0006052"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f24f3f35-c2ed-4d32-9bb5-2d9cd1258da6",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}