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

Abstract

Eigenvalue density generated by embedded Gaussian unitary ensemble with $k$-body interactions for two species (say $\pi$ and $\nu$) fermion systems is investigated by deriving formulas for the lowest six moments. Assumed in constructing this ensemble, called EGUE($k:\pi \nu$), is that the $\pi$ fermions ($m_1$ in number) occupy $N_1$ number of degenerate single particle (sp) states and similarly $\nu$ fermions ($m_2$ in number) in $N_2$ 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($k:\pi \nu$) formalism and results are extended to two species boson systems. 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.

21 pages, 3 figures, version accepted for publication in J. Stat. Mech. (2023)

References in corpus (13)

• Nuclear matrix elements for double-β decay
• Timescales in the quench dynamics of many-body quantum systems: Participation ratio vs out-of-time ordered correlator
• Structure of two-component Bose-Einstein condensates with respective vortex-antivortex superposition states
• Emergence of symmetry from random n-body interactions
• Particle Diagrams and Statistics of Many-Body Random Potentials
• Average-fluctuation separation in energy levels in many-particle quantum systems with $k$-body interactions using $q$-Hermite polynomials
• Bivariate $q$-normal distribution for transition strengths distribution from many-particle random matrix ensembles generated by $k$-body interactions
• Structure of wavefunction for interacting bosons in mean-field with random $k$-body interactions
• A smooth transition towards a Tracy-Widom distribution for the largest eigenvalue of interacting $k$-body fermionic Embedded Gaussian Ensembles
• Statistical Nuclear Spectroscopy with $q$-normal and bivariate $q$-normal distributions and $q$-Hermite polynomials
• Thermalization in many-fermion quantum systems with one- plus random $k$-body interactions
• On the Unification of Random Matrix Theories
• Bivariate moments of the two-point correlation function for embedded Gaussian unitary ensemble with $k$-body interactions

Cited by in corpus (2)

• Proxy-$SU(4)$ symmetry in A=60-90 region
• Distribution of lowest eigenvalue in $k$-body bosonic random matrix ensembles