Two species k-body embedded Gaussian unitary ensembles: q-normal form of the eigenvalue density
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Eigenvalue density generated by 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:πν), is that the π fermions (m_1 in number) occupy N_1 number of degenerate single particle (sp) states and similarly ν 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:πν) 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.
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