89 research outputs found
Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions
When a Bose-Einstein condensed cloud of atoms is given some angular momentum,
it forms vortices arranged in structures with a discrete rotational symmetry.
For these vortex states, the Hilbert space of the exact solution separates into
a "primary" space related to the mean-field Gross-Pitaevskii solution and a
"complementary" space including the corrections beyond mean-field. Considering
a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we
demonstrate how this separation can be used to close the conceptual gap between
exact solutions for systems with only a few atoms and the thermodynamic limit
for which the mean-field is the correct leading-order approximation. Although
we illustrate this approach for the case of weak interactions, it is expected
to be more generally valid.Comment: 8 pages, 5 figure
The Onset of Chaos with a Quadrupole--Quadrupole Interaction
The transition from order to chaos in atomic nuclei has been studied
analytically and numerically using a quadrupole--quadrupole residual
interaction. This interaction leads to chaotic behaviour, but the critical
energy MeV, corresponding to the onset of chaos, is higher
than that of the experimental one.Comment: 14 pages, 5 figures (available upon request to the authors), LaTex,
DFPD/93/TH/73, to be published in Nuovo Cimento
On the criterion for Bose-Einstein condensation for particles in traps
We consider the criterion for Bose condensation for particles in a harmonic
trap. For a fixed angular momentum, the lowest energy state for a cloud of
bosons with attractive interactions is the ground state of the cloud with all
the angular momentum in the center-of-mass motion, and the one-particle reduced
density matrix generally does not have a single large eigenvalue, but a number
of them, suggesting that the state is an example of a fragmented condensate
(Wilkin, Gunn, and Smith, Phys. Rev. Lett. 80, 2265 (1998)). We show that a
convenient way to describe correlations in the system is by defining an
internal one-particle reduced density matrix, in which the center-of-mass
motion is eliminated, and that this has a single eigenvalue equal to the number
of particles for the problem considered here. Our considerations indicate that
care is necessary in formulating a criterion for Bose-Einstein condensation.Comment: 2 pages, RevTex, Submitted to Phys. Rev.
On phases in weakly interacting finite Bose systems
We study precursors of thermal phase transitions in finite systems of
interacting Bose gases. For weakly repulsive interactions there is a phase
transition to the one-vortex state. The distribution of zeros of the partition
function indicates that this transition is first order, and the precursors of
the phase transition are already displayed in systems of a few dozen bosons.
Systems of this size do not exhibit new phases as more vortices are added to
the system.Comment: 7 pages, 2 figure
Relativistic Mean Field Approach and the Pseudo-Spin Symmetry
Based on the Relativistic Mean Field (RMF) approach the existence of the
broken pseudo-spin symmetry is investigated. Both spherical RMF and constrained
deformed RMF calculations are carried out employing realistic Lagrangian
parameters for spherical and for deformed sample nuclei. The quasi - degenerate
pseudo-spin doublets are confirmed to exist near the fermi surface for both
spherical and deformed nuclei.Comment: 9 pages RevTex, 4 p.s figures, to appear in Phys. Rev. C as R.
Self-Consistent Velocity Dependent Effective Interactions
The theory of self-consistent effective interactions in nuclei is extended
for a system with a velocity dependent mean potential. By means of the field
coupling method, we present a general prescription to derive effective
interactions which are consistent with the mean potential. For a deformed
system with the conventional pairing field, the velocity dependent effective
interactions are derived as the multipole pairing interactions in
doubly-stretched coordinates. They are applied to the microscopic analysis of
the giant dipole resonances (GDR's) of , the first excited
states of Sn isotopes and the first excited states of Mo isotopes.
It is clarified that the interactions play crucial roles in describing the
splitting and structure of GDR peaks, in restoring the energy weighted sum
rule, and in reducing the values of .Comment: 35 pages, RevTeX, 7 figures (available upon request), to appear in
Phys.Rev.
The pseudo-spin symmetry in Zr and Sn isotopes from the proton drip line to the neutron drip line
Based on the Relativistic continuum Hartree-Bogoliubov (RCHB) theory, the
pseudo-spin approximation in exotic nuclei is investigated in Zr and Sn
isotopes from the proton drip line to the neutron drip line. The quality of the
pseudo-spin approximation is shown to be connected with the competition between
the centrifugal barrier (CB) and the pseudo-spin orbital potential (PSOP). The
PSOP depends on the derivative of the difference between the scalar and vector
potentials . If , the pseudo-spin symmetry is exact. The
pseudo-spin symmetry is found to be a good approximation for normal nuclei and
to become much better for exotic nuclei with highly diffuse potential, which
have . The energy splitting of the pseudo-spin partners is
smaller for orbitals near the Fermi surface (even in the continuum) than the
deeply bound orbitals. The lower components of the Dirac wave functions for the
pseudo-spin partners are very similar and almost equal in magnitude.Comment: 22 pages, 9figure
Vortex stabilization in a small rotating asymmetric Bose-Einstein condensate
We use a variational method to investigate the ground-state phase diagram of
a small, asymmetric Bose-Einstein condensate with respect to the dimensionless
interparticle interaction strength and the applied external rotation
speed . For a given , the transition lines between no-vortex
and vortex states are shifted toward higher relative to those for the
symmetric case. We also find a re-entrant behavior, where the number of vortex
cores can decrease for large . In addition, stabilizing a vortex in a
rotating asymmetric trap requires a minimum interaction strength. For a given
asymmetry, the evolution of the variational parameters with increasing
shows two different types of transitions (sharp or continuous), depending on
the strength of the interaction. We also investigate transitions to states with
higher vorticity; the corresponding angular momentum increases continuously as
a function of
Nucleon-nucleon correlations and the single-particle strength in atomic nuclei
We propose a phenomenological approach to examine the role of short- and
long-range nucleon-nucleon correlations in the quenching of single-particle
strength in atomic nuclei and their evolution in asymmetric nuclei and neutron
matter. These correlations are thought to be the reason for the quenching of
spectroscopic factors observed in , and transfer
reactions. We show that the recently observed increase of the high-momentum
component of the protons in neutron-rich nuclei is consistent with the reduced
proton spectroscopic factors. Our approach connects recent results on
short-range correlations from high-energy electron scattering experiments with
the quenching of spectroscopic factors and addresses for the first time
quantitatively this intriguing question in nuclear physics, in particular
regarding its isospin dependence. We also speculate about the nature of a {\sl
quasi-proton} (nuclear polaron) in neutron matter and its kinetic energy, an
important quantity for the properties of neutron stars
Pairing in nuclear systems: from neutron stars to finite nuclei
We discuss several pairing-related phenomena in nuclear systems, ranging from
superfluidity in neutron stars to the gradual breaking of pairs in finite
nuclei. We focus on the links between many-body pairing as it evolves from the
underlying nucleon-nucleon interaction and the eventual experimental and
theoretical manifestations of superfluidity in infinite nuclear matter and of
pairing in finite nuclei. We analyse the nature of pair correlations in nuclei
and their potential impact on nuclear structure experiments. We also describe
recent experimental evidence that points to a relation between pairing and
phase transitions (or transformations) in finite nuclear systems. Finally, we
discuss recent investigations of ground-state properties of random two-body
interactions where pairing plays little role although the interactions yield
interesting nuclear properties such as 0+ ground states in even-even nuclei.Comment: 74 pages, 33 figs, uses revtex4. Submitted to Reviews of Modern
Physic
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