522 research outputs found
Restoration of particle number as a good quantum number in BCS theory
As shown in previous work, number projection can be carried out analytically
for states defined in a quasi-particle scheme when the states are expressed in
a coherent state representation. The wave functions of number-projected states
are well-known in the theory of orthogonal polynomials as Schur functions.
Moreover, the functions needed in pairing theory are a particularly simple
class of Schur functions that are easily constructed by means of recursion
relations. It is shown that complete sets of states can be projected from
corresponding quasi-particle states and that such states retain many of the
properties of the quasi-particle states from which they derive. It is also
shown that number projection can be used to construct a complete set of
orthogonal states classified by generalized seniority for any nucleus.Comment: 21 pages, 2 figures, epsf.def style file for printing figure
Extension of random-phase approximation preserving energy weighted sum rules: an application to a 3-level Lipkin model
A limitation common to all extensions of random-phase approximation including
only particle-hole configurations is that they violate to some extent the
energy weighted sum rules. Considering one such extension, the improved RPA
(IRPA), already used to study the electronic properties of metallic clusters,
we show how it can be generalized in order to eliminate this drawback. This is
achieved by enlarging the configuration space, including also elementary
excitations corresponding to the annihilation of a particle (hole) and the
creation of another particle (hole) on the correlated ground state. The
approach is tested within a solvable 3-level model.Comment: 2 figure
A computationally tractable version of the collective model
A computationally tractable version of the Bohr-Mottelson collective model is
presented which makes it possible to diagonalize realistic collective models
and obtain convergent results in relatively small appropriately chosen
subspaces of the collective model Hilbert space. Special features of the
proposed model is that it makes use of the beta wave functions given
analytically by the softened-beta version of the Wilets-Jean model, proposed by
Elliott et al., and a simple algorithm for computing SO(5) > SO(3) spherical
harmonics. The latter has much in common with the methods of Chacon, Moshinsky,
and Sharp but is conceptually and computationally simpler. Results are
presented for collective models ranging from the sherical vibrator to the
Wilets-Jean and axially symmetric rotor-vibrator models.Comment: 16 pages, 9 figure
Theories for multiple resonances
Two microscopic theories for multiple resonances in nuclei are compared,
n-particle-hole RPA and quantized Time-Dependent Hartree-Fock (TDHF). The
Lipkin-Meshkov-Glick model is used as test case. We find that quantized TDHF is
superior in many respects, except for very small systems.Comment: 14 Pages, 3 figures available upon request
Construction of SO(5)>SO(3) spherical harmonics and Clebsch-Gordan coefficients
The SO(5)>SO(3) spherical harmonics form a natural basis for expansion of
nuclear collective model angular wave functions. They underlie the
recently-proposed algebraic method for diagonalization of the nuclear
collective model Hamiltonian in an SU(1,1)xSO(5) basis. We present a computer
code for explicit construction of the SO(5)>SO(3) spherical harmonics and use
them to compute the Clebsch-Gordan coefficients needed for collective model
calculations in an SO(3)-coupled basis. With these Clebsch-Gordan coefficients
it becomes possible to compute the matrix elements of collective model
observables by purely algebraic methods.Comment: LaTeX (RevTeX), 15 pages; to be published in Computer Phys. Comm
RPA approach to rotational symmetry restoration in a three-level Lipkin model
We study an extended Lipkin-Meshkov-Glick model that permits a transition to
a deformed phase with a broken continuous symmetry. Unlike simpler models, one
sees a persistent zero-frequency Goldstone mode past the transition point into
the deformed phase. We found that the RPA formula for the correlation energy
provides a useful correction to the Hartree-Fock energy when the number of
particle N satisfies N > 3, and becomes accurate for large N. We conclude that
the RPA correlation energy formula offers a promising way to improve the
Hartree-Fock energy in a systematic theory of nuclear binding energies.Comment: RevTex, 11 pages, 3 postscript figure
Partial Dynamical Symmetry in the Symplectic Shell Model
We present an example of a partial dynamical symmetry (PDS) in an interacting
fermion system and demonstrate the close relationship of the associated
Hamiltonians with a realistic quadrupole-quadrupole interaction, thus shedding
new light on this important interaction. Specifically, in the framework of the
symplectic shell model of nuclei, we prove the existence of a family of
fermionic Hamiltonians with partial SU(3) symmetry. We outline the construction
process for the PDS eigenstates with good symmetry and give analytic
expressions for the energies of these states and E2 transition strengths
between them. Characteristics of both pure and mixed-symmetry PDS eigenstates
are discussed and the resulting spectra and transition strengths are compared
to those of real nuclei. The PDS concept is shown to be relevant to the
description of prolate, oblate, as well as triaxially deformed nuclei.
Similarities and differences between the fermion case and the previously
established partial SU(3) symmetry in the Interacting Boson Model are
considered.Comment: 9 figure
Association between symptoms of sleep apnea and problem behaviors in young adult twins and siblings
Background: Sleep apnea is one of the most common sleep disorders and it is related to multiple negative health consequences. Previous studies have shown that sleep apnea is influenced by genetic factors. However, studies have not investigated the genetic and environmental influences of symptoms of sleep apnea in young adults. Furthermore, the underpinnings of the relationship between apnea symptoms and internalizing/externalizing problems are unknown. The objectives of this study were to estimate the magnitude of: 1) genetic and environmental influences on self-reported apnea symptoms; 2) the relationship between self-reported apnea symptoms and internalizing/externalizing traits; 3) genetic and environmental influences on the associations between self-reported apnea symptoms, internalizing behaviors and externalizing behaviors.
Methods: In a twin/sibling study, univariate and multivariate models were fitted to estimate both individual variance and sources of covariance between symptoms of sleep apnea and internalizing/externalizing behaviors.
Results: Our results show that genetic influences account for 40% the variance in sleep apnea symptoms. Moreover, there are modest associations between depression, anxiety and externalizing behaviors with apnea symptoms (ranging from r = .22 to .29). However, the origins of these associations differ. For example, whereas most of the covariation between symptoms of depression and sleep apnea can be explained by genes (95%), there was a larger role for the environment (53%) in the association between symptoms of anxiety and sleep apnea.
Conclusions: Genetic factors explain a significant proportion of variance in symptoms of apnea and most of the covariance with depression
Entanglement between motional states of a single trapped ion and light
We propose a generation method of Bell-type states involving light and the
vibrational motion of a single trapped ion. The trap itself is supposed to be
placed inside a high- cavity sustaining a single mode, quantized
electromagnetic field. Entangled light-motional states may be readily generated
if a conditional measurement of the ion's internal electronic state is made
after an appropriate interaction time and a suitable preparation of the initial
state. We show that all four Bell states may be generated using different
motional sidebands (either blue or red), as well as adequate ionic relative
phases.Comment: 4 pages, LaTe
Self Consistent and Renormalized particle-particle RPA in a Schematic Model
The dynamical effects of ground state correlations for excitation energies
and transition strengths near the superfluid phase transition are studied in
the soluble two level pairing model, in the context of the particle-particle
self consistent Random Phase Approximation (SCRPA). Exact results are well
reproduced across the transition region, beyond the collapse of the standard
particle-particle Random Phase Approximation. The effects of two-body
correlation in the SCRPA are displayed explicitly.Comment: 11 pages, revtex, 3ps figures, to appear in Phys. Rev.
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