{
  "annotation_id": "13705ee1-149e-4ef8-8c1d-1b89241e13d1",
  "date_created": "2026-03-02T18:00:46.021000Z",
  "date_modified": "2026-03-02T18:00:46.021000Z",
  "file_hash": "8f23f7a64845f2fe08bce706056f84053816dc24d84b863c7591ebb4bce6d456",
  "private": false,
  "record": {
    "abstract": "A generalized version of the Kato-Bloch perturbation expansion is presented.\nIt consists of replacing simple numbers appearing in the perturbative series by\nmatrices. This leads to the fact that the dependence of the eigenvalues of the\nperturbed system on the strength of the perturbation is not necessarily\npolynomial. The efficiency of the matrix expansion is illustrated in three\ncases: the Mathieu equation, the anharmonic oscillator and weakly coupled\nHeisenberg chains. It is shown that the matrix expansion converges for a\nsuitably chosen subspace and, for weakly coupled Heisenberg chains, it can lead\nto an ordered state starting from a disordered single chain. This test is\nusually failed by conventional perturbative approaches.",
    "arxiv_id": "physics/0312011",
    "authors": [
      "S. Moukouri"
    ],
    "categories": [
      "physics.comp-ph",
      "cond-mat.str-el"
    ],
    "doi": "10.1016/j.physleta.2004.03.066",
    "title": "A Matrix Kato-Bloch Perturbation Method for Hamiltonian Systems",
    "url": "https://arxiv.org/abs/physics/0312011"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "37b3b63d-6c25-441e-834f-2ea071b7d821",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}