{
  "abstract": "Embedded random matrix ensembles operating in nuclear shell model spaces, with nucleons occupying a finite set of single particle orbits and interacting via a two-body interaction, form the basis for statistical shell model. With sufficiently strong interaction, the level densities in shell model spaces take close to a Gaussian form and transition strength distributions close to a bivariate Gaussian form. In practice, partitioning via spherical configurations ($\\tilde{m}$) and angular momentum $J$ (also isospin where appropriate) are essential. The resulting statistical spectroscopy or statistical shell model was applied successfully in the past in some studies of nuclear level densities, orbit occupancies, $β$-decay matrix elements and so on. Going beyond these, recently it is recognized that embedded ensembles, in a better approximation, generate in-fact $q$-normal form ($q=1$ gives Gaussian and $q=0$ Wigner's semi-circle) for density of eigenvalues, bivariate $q$-normal form for transition strengths and conditional $q$-normal form for strength functions. These then allow us to develop statistical shell model with $q$-normal forms. These new developments in embedded ensembles and statistical shell model are briefly reviewed in this paper. Also described, using some examples, is the role of the $q$ parameter in generating statistical properties of general quantum many-particle systems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.29210",
  "author_total": 3,
  "authors": [
    {
      "name": "V. K. B. Kota"
    },
    {
      "name": "N. D. Chavda"
    },
    {
      "name": "Manan Vyas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2nw2nmsera06c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.29210",
  "fulltext_url": null,
  "id": "2nw2nmsera06c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.29210",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "nucl-th"
    ],
    [
      "arxiv",
      "quant-ph"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2606.29210",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2nw2nmsera06c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2606.29210",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.29210"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:nucl-th",
      "subfield": "nuclear"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Embedded Random Matrix Ensembles to Statistical Shell Model: Operation of $q$-normal forms",
  "title_text": "Embedded Random Matrix Ensembles to Statistical Shell Model: Operation of q-normal forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/2nw2nmsera06c",
  "venue": "arXiv",
  "versions": []
}