{
  "annotation_id": "a57cf176-c0da-4fec-a025-fe8365e1242c",
  "date_created": "2026-03-02T18:00:25.753000Z",
  "date_modified": "2026-03-02T18:00:25.753000Z",
  "file_hash": "9dd522c0e4c06ca2f053ce0860bbb599c7f3151863daa2dadf63463cf8a392c7",
  "private": false,
  "record": {
    "abstract": "We consider the Gaussian ensembles of random matrices and describe the normal\nmodes of the eigenvalue spectrum, i.e., the correlated fluctuations of\neigenvalues about their most probable values. The associated normal mode\nspectrum is linear, and for large matrices, the normal modes are found to be\nChebyshev polynomials of the second kind. We contrast this with the behaviour\nof a sequence of uncorrelated levels, which has a quadratic normal mode\nspectrum. The difference in the rigidity of random matrix spectra and sequences\nof uncorrelated levels can be attributed to this difference in the normal mode\nspectra. We illustrate this by calculating the number variance in the two\ncases.",
    "arxiv_id": "nucl-th/9812037",
    "authors": [
      "A. Andersen",
      "A. D. Jackson",
      "H. J. Pedersen"
    ],
    "categories": [
      "nucl-th",
      "cond-mat",
      "hep-th"
    ],
    "doi": "10.1016/S0375-9474(99)00101-3",
    "journal_ref": "Nucl.Phys. A650 (1999) 213-223",
    "title": "Rigidity and Normal Modes in Random Matrix Spectra",
    "url": "https://arxiv.org/abs/nucl-th/9812037"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "cb99f9c8-8a27-4251-8ba9-5c11a6ec3898",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}