1,090 research outputs found
Random matrix ensemble with random two-body interactions in presence of a mean-field for spin one boson systems
For number of bosons, carrying spin (=1) degree of freedom, in
number of single particle orbitals, each triply degenerate, we
introduce and analyze embedded Gaussian orthogonal ensemble of random matrices
generated by random two-body interactions that are spin (S) scalar
[BEGOE(2)-]. The embedding algebra is with SO(3) generating spin . A method for constructing the ensembles
in fixed-(, ) space has been developed. Numerical calculations show that
the form of the fixed-(, ) density of states is close to Gaussian and
level fluctuations follow GOE. Propagation formulas for the fixed-(, )
space energy centroids and spectral variances are derived for a general one
plus two-body Hamiltonian preserving spin. In addition to these, we also
introduce two different pairing symmetry algebras in the space defined by
BEGOE(2)- and the structure of ground states is studied for each paring
symmetry.Comment: 22 pages, 6 figure
O(12) limit and complete classification of symmetry schemes in proton-neutron interacting boson model
It is shown that the proton-neutron interacting boson model (pnIBM) admits
new symmetry limits with O(12) algebra which break F-spin but preserves the
quantum number M_F. The generators of O(12) are derived and the quantum number
`v' of O(12) for a given boson number N is determined by identifying the
corresponding quasi-spin algebra. The O(12) algebra generates two symmetry
schemes and for both of them, complete classification of the basis states and
typical spectra are given. With the O(12) algebra identified, complete
classification of pnIBM symmetry limits with good M_F is established.Comment: 22 pages, 1 figur
Spectral analysis of molecular resonances in erbium isotopes: Are they close to semi-Poisson?
We perform a thorough analysis of the spectral statistics of experimental
molecular resonances, of bosonic erbium Er and Er isotopes,
produced as a function of magnetic field() by Frisch et al. [Nature 507,
(2014) 475], utilizing some recently derived surmises which interpolate between
Poisson and GOE and without unfolding. Supplementing this with an analysis
using unfolded spectrum, it is shown that the resonances are close to
semi-Poisson distribution. There is an earlier claim of missing resonances by
Molina et al. [Phys. Rev. E 92, (2015) 042906]. These two interpretations can
be tested by more precise measurements in future experiments.Comment: 7 pages, 6 figure
Bivariate -distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems
Interacting many-particle systems with a mean-field one body part plus a
chaos generating random two-body interaction having strength , exhibit
Poisson to GOE and Breit-Wigner (BW) to Gaussian transitions in level
fluctuations and strength functions with transition points marked by
and , respectively; . For these systems theory for matrix elements of one-body transition
operators is available, as valid in the Gaussian domain, with , in terms of orbitals occupation numbers, level densities and an
integral involving a bivariate Gaussian in the initial and final energies. Here
we show that, using bivariate -distribution, the theory extends below from
the Gaussian regime to the BW regime up to . This is well
tested in numerical calculations for six spinless fermions in twelve single
particle states.Comment: 7 pages, 2 figure
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