Two-species k-body embedded Gaussian unitary ensembles: q-normal form of the eigenvalue density

• Published in: Journal of statistical mechanics Vol. 2023; no. 9; pp. 93103 - 93121
• Main Authors: Vyas, Manan, Kota, V K B
• Format: Journal Article
• Language: English
• Published: IOP Publishing 01.09.2023
• Subjects: q-normal distributions; random matrix theory and extensions; statistical nuclear spectroscopy; two species many-body quantum systems
• ISSN: 1742-5468; 1742-5468
• DOI: 10.1088/1742-5468/acf854

Abstract The eigenvalue density generated by an embedded Gaussian unitary ensemble with k -body interactions for two-species (say π and ν ) fermion systems is investigated by deriving formulas for the lowest six moments. Assumed in constructing this ensemble, called EGUE( k : π ν ), is that the π fermions ( m 1 in number) occupy N 1 number of degenerate single particle (sp) states, and similarly the ν fermions ( m 2 in number) occupy N 2 number of degenerate sp states. The Hamiltonian is assumed to be k -body preserving ( m 1 , m 2 ) . Formulas with finite ( N 1 , N 2 ) corrections and asymptotic limit formulas both show that the eigenvalue density takes q -normal form with the q parameter defined by the fourth moment. The EGUE( k : π ν ) formalism and results are extended to two-species boson systems. The results in this work show that the q -normal form of the eigenvalue density established only recently for identical fermion and boson systems extends to two-species fermion and boson systems.