{
  "annotation_id": "1f653cb0-c177-4a96-994c-3f5529c42299",
  "date_created": "2026-03-02T18:00:38.975000Z",
  "date_modified": "2026-03-02T18:00:38.975000Z",
  "file_hash": "b2f803220c1eab8e6581af3feac204737e0859529fa04b3170c8c5fcb954c1fe",
  "private": false,
  "record": {
    "abstract": "Homogenization theory is used to calculate the macroscopic dielectric\nconstant from the quantum microscopic dielectric function in a periodic medium.\nThe method can be used to calculate any macroscopic constitutive relation, but\nit is illustrated here for the case of electrodynamics of matter. The so-called\ncell problem of homogenization theory is solved and an explicit expression is\ngiven for the macroscopic dielectric constant in a form akin to the\nClausius-Mossotti or Lorentz-Lorenz relation. The validity of this expression\nis checked by showing that the macroscopic dielectric constant is causal and\nhas the expected symmetry properties, and that the average of the microscopic\nenergy density is the macroscopic one. Finally, the general expression is\napplied to Bloch eigenstates. Finally, the corresponding many-body problem is\nbriefly discussed.",
    "arxiv_id": "physics/0201035",
    "authors": [
      "Christian Brouder",
      "Stephanie Rossano"
    ],
    "categories": [
      "physics.class-ph"
    ],
    "doi": "10.1140/epjb/e2005-00160-1",
    "journal_ref": "Euro. J. Phys. B 45 (2005) 19-31",
    "title": "Microscopic Calculation of the Constitutive Relations",
    "url": "https://arxiv.org/abs/physics/0201035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "78b90f20-30e4-4493-ab1c-a076e5e5e965",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}