2015/04/03 by V. K. B. Kota, Kota, V. K. B., Manan Vyas +1 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Nuclear Theory (nucl-th) #Quantum Physics (quant-ph) #Random Matrices and Applications #Scientific Research and Discoveries #Statistical Mechanics and Entropy #math-ph #math.MP #nucl-th #quant-ph
paper · pdf · doi:10.48550/arxiv.1504.00759
65 pages, 5 figures, 4 tables; some sections of the paper overlap considerably with the arXiv papers 1106.0395, 1411.6391 and 1501.07670
arxiv created 2015/04/03 · openalex publication_date 2015/04/03 · arxiv updated 2015/04/06 · openalex created_date 2022/09/19 · openalex updated_date 2026/07/28
Embedded random matrix ensembles are generic models for describing statistical properties of finite isolated interacting quantum many-particle systems. For the simplest spinless systems, with say m particles in N single particle states and interacting via k-body interactions, we have EGUE(k) and the embedding algebra is U(N). A finite quantum system, induced by a transition operator, makes transitions from its states to the states of the same system or to those of another system. Examples are electromagnetic transitions (same initial and final systems), nuclear beta and double beta decay (different initial and final systems), particle addition to/removal from a given system and so on. Towards developing a complete statistical theory for transition strength densities, we have derived formulas for lower order bivariate moments of the strength densities generated by a variety of transition operators. For a spinless fermion system, using EGUE(k) representation for Hamiltonian and an independent EGUE(t) representation for transition operator, finite-N formulas for moments up to order four are derived, for the first time, for the transition strength densities. Formulas for the moments up to order four are also derived for systems with two types of spinless fermions and a transition operator similar to beta decay and neutrinoless beta decay operators. Moments formulas are also derived for transition operator that removes k0 number of particles from m fermion system. Numerical results obtained using the exact formulas for two-body (k=2) Hamiltonians (in some examples for k=3,4) and the asymptotic formulas clearly establish that in general the smoothed form of the bivariate transition strength densities take bivariate Gaussian form for isolated finite quantum systems. Extensions of these results to bosonic systems and EGUE ensembles with further symmetries are discussed.