{
  "annotation_id": "e89c7b5b-b963-424a-aa44-f27c42fbd77b",
  "date_created": "2026-03-02T18:02:38.020000Z",
  "date_modified": "2026-03-02T18:02:38.020000Z",
  "file_hash": "e576ff5c8cb4f39c8a27742983be9100f9e874c807fd5d542b4bd5f5046aefec",
  "private": false,
  "record": {
    "abstract": "Employing the path integral approach, we calculate the semiclassical\nequilibrium density matrix of a particle moving in a nonlinear potential field\nfor coordinates near the top of a potential barrier. As the temperature is\ndecreased, near a critical temperature $T_c$ the harmonic approximation for the\nfluctuation path integral fails. This is due to a caustic arising at a\nbifurcation point of the classical paths. We provide a selfconsistent scheme to\ntreat the large quantum fluctuations leading to a nonlinear fluctuation\npotential. The procedure differs from methods used near caustics of the real\ntime propagator. The semiclassical density matrix is determined explicitly for\nthe case of asymmetric barriers from high temperatures down to temperatures\nsomewhat below $T_c$.\n  Pacs: 03.65.Sq, 05.30.-d",
    "arxiv_id": "quant-ph/9512015",
    "authors": [
      "F. J. Weiper",
      "J. Ankerhold",
      "H. Grabert"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/0378-4371(95)00297-9",
    "journal_ref": "Physica A223 (1996) 193",
    "title": "Semiclassical Density Matrix Near the Top of a Barrier",
    "url": "https://arxiv.org/abs/quant-ph/9512015"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8223bc01-c70e-4f7e-9d14-df449dbcac3b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}