Embedded Random Matrix Ensembles to Statistical Shell Model: Operation of q-normal forms
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 (m̃) 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.
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BibTeX
@misc{kota2026embedded,
title = {{Embedded Random Matrix Ensembles to Statistical Shell Model: Operation of $q$-normal forms}},
author = {V. K. B. Kota and N. D. Chavda and Manan Vyas},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.29210},
eprint = {2606.29210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.29210},
}
RIS
TY - UNPB
TI - Embedded Random Matrix Ensembles to Statistical Shell Model: Operation of q-normal forms
AU - V. K. B. Kota
AU - N. D. Chavda
AU - Manan Vyas
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2606.29210
UR - https://arxiv.org/abs/2606.29210
AB - 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 (m̃) 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.
ER -