15,132 research outputs found

### Extending PT symmetry from Heisenberg algebra to E2 algebra

The E2 algebra has three elements, J, u, and v, which satisfy the commutation
relations [u,J]=iv, [v,J]=-iu, [u,v]=0. We can construct the Hamiltonian
H=J^2+gu, where g is a real parameter, from these elements. This Hamiltonian is
Hermitian and consequently it has real eigenvalues. However, we can also
construct the PT-symmetric and non-Hermitian Hamiltonian H=J^2+igu, where again
g is real. As in the case of PT-symmetric Hamiltonians constructed from the
elements x and p of the Heisenberg algebra, there are two regions in parameter
space for this PT-symmetric Hamiltonian, a region of unbroken PT symmetry in
which all the eigenvalues are real and a region of broken PT symmetry in which
some of the eigenvalues are complex. The two regions are separated by a
critical value of g.Comment: 8 pages, 7 figure

### Microscopic models for exotic nuclei

Starting from successful self-consistent mean-field models, this paper
discusses why and how to go beyond the mean field approximation. To include
long-range correlations from fluctuations in collective degrees of freedom, one
has to consider symmetry restoration and configuration mixing, which give
access to ground-state correlations and spectroscopy.Comment: invited talk at ENAM0

### Comment on ``Structure of exotic nuclei and superheavy elements in a relativistic shell model''

A recent paper [M. Rashdan, Phys. Rev. C 63, 044303 (2001)] introduces the
new parameterization NL-RA1 of the relativistic mean-field model which is
claimed to give a better description of nuclear properties than earlier ones.
Using this model ^{298}114 is predicted to be a doubly-magic nucleus. As will
be shown in this comment these findings are to be doubted as they are obtained
with an unrealistic parameterization of the pairing interaction and neglecting
ground-state deformation.Comment: 2 pages REVTEX, 3 figures, submitted to comment section of Phys. Rev.
C. shortened and revised versio

### Systematics of quadrupolar correlation energies

We calculate correlation energies associated with the quadrupolar shape
degrees of freedom with a view to improving the self-consistent mean-field
theory of nuclear binding energies. The Generator Coordinate Method is employed
using mean-field wave functions and the Skyrme SLy4 interaction. Systematic
results are presented for 605 even-even nuclei of known binding energies, going
from mass A=16 up to the heaviest known. The correlation energies range from
0.5 to 6.0 MeV in magnitude and are rather smooth except for large variations
at magic numbers and in light nuclei. Inclusion of these correlation energies
in the calculated binding energy is found to improve two deficiencies of the
Skyrme mean field theory. The pure mean field theory has an exaggerated shell
effect at neutron magic numbers and addition of the correlation energies reduce
it. The correlations also explain the phenomenon of mutually enhanced magicity,
an interaction between neutron and proton shell effects that is not explicable
in mean field theory.Comment: 4 pages with 3 embedded figure

### Applications of PTTI to new techniques for determining crustal movements, polar motion, and the rotation of the earth

New extra-terrestrial techniques are discussed for geodesy and geodynamics include laser range measurements to the moon or to artificial satellites, Doppler measurements with the Transit satellite system, and both independent-clock and linked-antenna microwave interferometry. The ways in which PTTI measurements are used in these techniques will be reviewed, and the accuracies expected during the latter half of the 1970's will be discussed. At least 3 of the techniques appear capable of giving accuracies of 5 cm or better in each coordinate for many points on the earth's surface, and comparable accuracies for the earth's rotation and polar motion. For fixed stations or for sites a few hundred km apart, baseline lengths accurate to 1 cm may be achieved. Ways in which the complementary aspects of the different techniques can be exploited will be discussed, as well as how they tie in with improved ground techniques for determining crustal movements. Some recent results from the extra-terrestrial methods will be mentioned

### Calculation of the Hidden Symmetry Operator for a \cP\cT-Symmetric Square Well

It has been shown that a Hamiltonian with an unbroken \cP\cT symmetry also
possesses a hidden symmetry that is represented by the linear operator \cC.
This symmetry operator \cC guarantees that the Hamiltonian acts on a Hilbert
space with an inner product that is both positive definite and conserved in
time, thereby ensuring that the Hamiltonian can be used to define a unitary
theory of quantum mechanics. In this paper it is shown how to construct the
operator \cC for the \cP\cT-symmetric square well using perturbative
techniques.Comment: 10 pages, 2 figure

### Symmetry restoration for odd-mass nuclei with a Skyrme energy density functional

In these proceedings, we report first results for particle-number and
angular-momentum projection of self-consistently blocked triaxial
one-quasiparticle HFB states for the description of odd-A nuclei in the context
of regularized multi-reference energy density functionals, using the entire
model space of occupied single-particle states. The SIII parameterization of
the Skyrme energy functional and a volume-type pairing interaction are used.Comment: 8 pages, 3 figures, workshop proceeding

### Quantum counterpart of spontaneously broken classical PT symmetry

The classical trajectories of a particle governed by the PT-symmetric
Hamiltonian $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) have been studied in
depth. It is known that almost all trajectories that begin at a classical
turning point oscillate periodically between this turning point and the
corresponding PT-symmetric turning point. It is also known that there are
regions in $\epsilon$ for which the periods of these orbits vary rapidly as
functions of $\epsilon$ and that in these regions there are isolated values of
$\epsilon$ for which the classical trajectories exhibit spontaneously broken PT
symmetry. The current paper examines the corresponding quantum-mechanical
systems. The eigenvalues of these quantum systems exhibit characteristic
behaviors that are correlated with those of the associated classical system.Comment: 11 pages, 7 figure

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