934 research outputs found
GW approximation with self-screening correction
The \emph{GW} approximation takes into account electrostatic self-interaction
contained in the Hartree potential through the exchange potential. However, it
has been known for a long time that the approximation contains self-screening
error as evident in the case of the hydrogen atom. When applied to the hydrogen
atom, the \emph{GW} approximation does not yield the exact result for the
electron removal spectra because of the presence of self-screening: the hole
left behind is erroneously screened by the only electron in the system which is
no longer present. We present a scheme to take into account self-screening and
show that the removal of self-screening is equivalent to including exchange
diagrams, as far as self-screening is concerned. The scheme is tested on a
model hydrogen dimer and it is shown that the scheme yields the exact result to
second order in where and are respectively
the onsite and offsite Hubbard interaction parameters and the hopping
parameter.Comment: 9 pages, 2 figures; Submitted to Phys. Rev.
Normal Modes of a Vortex in a Trapped Bose-Einstein Condensate
A hydrodynamic description is used to study the normal modes of a vortex in a
zero-temperature Bose-Einstein condensate. In the Thomas-Fermi (TF) limit, the
circulating superfluid velocity far from the vortex core provides a small
perturbation that splits the originally degenerate normal modes of a
vortex-free condensate. The relative frequency shifts are small in all cases
considered (they vanish for the lowest dipole mode with |m|=1), suggesting that
the vortex is stable. The Bogoliubov equations serve to verify the existence of
helical waves, similar to those of a vortex line in an unbounded weakly
interacting Bose gas. In the large-condensate (small-core) limit, the
condensate wave function reduces to that of a straight vortex in an unbounded
condensate; the corresponding Bogoliubov equations have no bound-state
solutions that are uniform along the symmetry axis and decay exponentially far
from the vortex core.Comment: 15 pages, REVTEX, 2 Postscript figures, to appear in Phys. Rev. A. We
have altered the material in Secs. 3B and 4 in connection with the normal
modes that have |m|=1. Our present treatment satisfies the condition that the
fundamental dipole mode of a condensate with (or without) a vortex should
have the bare frequency $\omega_\perp
Statistical mechanics of Floquet systems: the pervasive problem of near degeneracies
The statistical mechanics of periodically driven ("Floquet") systems in
contact with a heat bath exhibits some radical differences from the traditional
statistical mechanics of undriven systems. In Floquet systems all quasienergies
can be placed in a finite frequency interval, and the number of near
degeneracies in this interval grows without limit as the dimension N of the
Hilbert space increases. This leads to pathologies, including drastic changes
in the Floquet states, as N increases. In earlier work these difficulties were
put aside by fixing N, while taking the coupling to the bath to be smaller than
any quasienergy difference. This led to a simple explicit theory for the
reduced density matrix, but with some major differences from the usual time
independent statistical mechanics. We show that, for weak but finite coupling
between system and heat bath, the accuracy of a calculation within the
truncated Hilbert space spanned by the N lowest energy eigenstates of the
undriven system is limited, as N increases indefinitely, only by the usual
neglect of bath memory effects within the Born and Markov approximations. As we
seek higher accuracy by increasing N, we inevitably encounter quasienergy
differences smaller than the system-bath coupling. We therefore derive the
steady state reduced density matrix without restriction on the size of
quasienergy splittings. In general, it is no longer diagonal in the Floquet
states. We analyze, in particular, the behavior near a weakly avoided crossing,
where quasienergy near degeneracies routinely appear. The explicit form of our
results for the denisty matrix gives a consistent prescription for the
statistical mechanics for many periodically driven systems with N infinite, in
spite of the Floquet state pathologies.Comment: 31 pages, 3 figure
Vortex Waves in a Cloud of Bose Einstein - Condensed, Trapped Alkali - Metal Atoms
We consider the vortex state solution for a rotating cloud of trapped, Bose
Einstein - condensed alkali atoms and study finite temperature effects. We find
that thermally excited vortex waves can distort the vortex state significantly,
even at the very low temperatures relevant to the experiments.Comment: to appear in Phys. Rev.
Beyond the Thomas-Fermi approximation for a trapped condensed Bose-Einstein gas
Corrections to the zero-temperature Thomas-Fermi description of a dilute
interacting condensed Bose-Einstein gas confined in an isotropic harmonic trap
arise due to the presence of a boundary layer near the condensate surface.
Within the Bogoliubov approximation, the various contributions to the
ground-state condensate energy all have terms of order R^{-4}ln R and R^{-4},
where R is the number-dependent dimensionless condensate radius in units of the
oscillator length. The zero-order hydrodynamic density-fluctuation amplitudes
are extended beyond the Thomas-Fermi radius through the boundary layer to
provide a uniform description throughout all space. The first-order correction
to the excitation frequencies is shown to be of order R^{-4}.Comment: 12 pages, 2 figures, revtex. Completely revised discussion of the
boundary-layer corrections to collective excitations, and two new figures
added. To appear in Phys. Rev. A (October, 1998
Unitarity potentials and neutron matter at the unitary limit
We study the equation of state of neutron matter using a family of unitarity
potentials all of which are constructed to have infinite scattering
lengths . For such system, a quantity of much interest is the ratio
where is the true ground-state energy of the system,
and is that for the non-interacting system. In the limit of
, often referred to as the unitary limit, this ratio is
expected to approach a universal constant, namely . In the
present work we calculate this ratio using a family of hard-core
square-well potentials whose can be exactly obtained, thus enabling us to
have many potentials of different ranges and strengths, all with infinite
. We have also calculated using a unitarity CDBonn potential
obtained by slightly scaling its meson parameters. The ratios given by
these different unitarity potentials are all close to each other and also
remarkably close to 0.44, suggesting that the above ratio is indifferent
to the details of the underlying interactions as long as they have infinite
scattering length. A sum-rule and scaling constraint for the renormalized
low-momentum interaction in neutron matter at the unitary limit is discussed.Comment: 7.5 pages, 7 figure
Off-axis vortices in trapped Bose condensed gases: angular momentum and frequency splitting
We consider non centered vortices and their arrays in a cylindrically trapped
Bose-Einstein condensate at zero temperature. We study the kinetic energy and
the angular momentum per particle in the Thomas Fermi regime and their
dependence on the distance of the vortices from the center of the trap. Using a
perturbative approach with respect to the velocity-field of the vortices, we
calculate to first order the frequency shift of the collective low-lying
excitations due to the presence of an off-center vortex or a vortex array, and
compare these results with predictions which would be obtained by the
application of a simple sum-rule approach, previously found to be very
successful for centered vortices. It turns out that the simple sum-rule
approach fails for off-centered vortices.Comment: 11 pages, LaTeX, 3 figures. Perturbative approach adde
Theory of coherent Bragg spectroscopy of a trapped Bose-Einstein condensate
We present a detailed theoretical analysis of Bragg spectroscopy from a
Bose-Einstein condensate at T=0K. We demonstrate that within the linear
response regime, both a quantum field theory treatment and a meanfield
Gross-Pitaevskii treatment lead to the same value for the mean evolution of the
quasiparticle operators. The observable for Bragg spectroscopy experiments,
which is the spectral response function of the momentum transferred to the
condensate, can therefore be calculated in a meanfield formalism. We analyse
the behaviour of this observable by carrying out numerical simulations in
axially symmetric three-dimensional cases and in two dimensions. An approximate
analytic expression for the observable is obtained and provides a means for
identifying the relative importance of three broadening and shift mechanisms
(meanfield, Doppler, and finite pulse duration) in different regimes. We show
that the suppression of scattering at small values of q observed by
Stamper-Kurn et al. [Phys. Rev. Lett. 83, 2876 (1999)] is accounted for by the
meanfield treatment, and can be interpreted in terms of the interference of the
u and v quasiparticle amplitudes. We also show that, contrary to the
assumptions of previous analyses, there is no regime for trapped condensates
for which the spectral response function and the dynamic structure factor are
equivalent. Our numerical calculations can also be performed outside the linear
response regime, and show that at large laser intensities a significant
decrease in the shift of the spectral response function can occur due to
depletion of the initial condensate.Comment: RevTeX4 format, 16 pages plus 7 eps figures; Update to published
version: minors changes and an additional figure. (To appear in Phys. Rev. A
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
Multiple electron-hole scattering effect on quasiparticle properties in a homogeneous electron gas
We present a detailed study of a contribution of the T matrix accounting for
multiple scattering between an electron and a hole to the quasiparticle
self-energy. This contribution is considered as an additional term to the GW
self-energy. The study is based on a variational solution of the T-matrix
integral equation within a local approximation. A key quantity of such a
solution, the local electron-hole interaction, is obtained at the small
four-momentum transfer limit. Performed by making use of this limit form,
extensive calculations of quasiparticle properties in the homogeneous electron
gas over a broad range of electron densities are reported. We carry out an
analysis of how the T-matrix contribution affects the quasiparticle damping
rate, the quasiparticle energy, the renormalization constant, and the effective
mass enhancement. We find that in comparison with the GW approximation the
inclusion of the T matrix leads to an essential increase of the damping rate, a
slight reduction of the GW band narrowing, a decrease of the renormalization
constant at the Fermi wave vector, and some "weighting" of quasiparticles at
the Fermi surface.Comment: 12 pages, 11 figures, 1 tabl
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