Abstract
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.
Subject
Statistics, Probability and Uncertainty,Statistics and Probability,Statistical and Nonlinear Physics