{
  "annotation_id": "f52b48ec-b078-4548-949d-76c0de8f3a52",
  "date_created": "2026-03-02T18:01:53.159000Z",
  "date_modified": "2026-03-02T18:01:53.159000Z",
  "file_hash": "217e2ba9d36d172926fb5e602a208f3c975756494ec6adfe89216a2fa6590350",
  "private": false,
  "record": {
    "abstract": "We calculate the rate of decrease of the expectation value of the transverse\ncomponent of spin for spin-1/2 particles in a magnetic field with a spatial\ngradient, to determine the conditions under which a previous classical\ndescription is valid. A density matrix treatment is required for two reasons.\nThe first arises because the particles initially are not in a pure state due to\nthermal motion. The second reason is that each particle interacts with the\nmagnetic field and the other particles, with the latter taken to be via a\n2-body central force. The equations for the 1-body Wigner distribution\nfunctions are written in a general manner, and the places where quantum\nmechanical effects can play a role are identified. One that may not have been\nconsidered previously concerns the momentum associated with the magnetic field\ngradient, which is proportional to the time integral of the gradient. Its\nrelative magnitude compared with the important momenta in the problem is a\nsignificant parameter, and if their ratio is not small some non-classical\neffects contribute to the solution.\n  Assuming the field gradient is sufficiently small, and a number of other\ninequalities are satisfied involving the mean wavelength, range of the force,\nand the mean separation between particles, we solve the integro- partial\ndifferential equations for the Wigner functions to second order in the strength\nof the gradient. When the same reasoning is applied to a different problem with\nno field gradient, but having instead a gradient to the z-component of\npolarization, the connection with the diffusion coefficient is established, and\nwe find agreement with the classical result for the rate of decrease of the\ntransverse component of magnetization.",
    "arxiv_id": "quant-ph/0208186",
    "authors": [
      "Leon Heller"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevB.67.094417",
    "title": "Classical Limit of Demagnetization in a Field Gradient",
    "url": "https://arxiv.org/abs/quant-ph/0208186"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "494eaa92-a8dc-4af9-af43-3b5b45f49365",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}