{
  "annotation_id": "044ba96b-b4a3-4e06-9d05-8e51edf7cf45",
  "date_created": "2026-03-02T18:01:21.748000Z",
  "date_modified": "2026-03-02T18:01:21.748000Z",
  "file_hash": "bb153ad75b87101f8c46a67ef63afad915e1e590d87f55c20ec9b78fb237a491",
  "private": false,
  "record": {
    "abstract": "We study the relative index of two orthogonal infinite dimensional\nprojections which, in the finite dimensional case, is the difference in their\ndimensions. We relate the relative index to the Fredholm index of appropriate\noperators, discuss its basic properties, and obtain various formulas for it. We\napply the relative index to counting the change in the number of electrons\nbelow the Fermi energy of certain quantum systems and interpret it as the\ncharge deficiency. We study the relation of the charge deficiency with the\nnotion of adiabatic charge transport that arises from the consideration of the\nadiabatic curvature. It is shown that, under a certain covariance,\n(homogeneity), condition the two are related. The relative index is related to\nBellissard\u0027s theory of the Integer Hall effect. For Landau Hamiltonians the\nrelative index is computed explicitly for all Landau levels.",
    "arxiv_id": "physics/9803014",
    "authors": [
      "Joseph E. Avron",
      "Ruedi Seiler",
      "Barry Simon"
    ],
    "categories": [
      "math-ph",
      "cond-mat.mes-hall",
      "math.MP",
      "physics.bio-ph"
    ],
    "doi": "10.1007/BF02102644",
    "journal_ref": "Comm.Math.Phys. 159, 399-422, (1994)",
    "title": "Charge Deficiency, Charge Transport and Comparison of Dimensions",
    "url": "https://arxiv.org/abs/physics/9803014"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3b21b7db-43c1-4d6a-bf30-45332d40f587",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}