250 research outputs found
Conserving and Gapless Approximations for an Inhomogeneous Bose Gas at Finite Temperatures
We derive and discuss the equations of motion for the condensate and its
fluctuations for a dilute, weakly interacting Bose gas in an external potential
within the self--consistent Hartree--Fock--Bogoliubov (HFB) approximation.
Account is taken of the depletion of the condensate and the anomalous Bose
correlations, which are important at finite temperatures. We give a critical
analysis of the self-consistent HFB approximation in terms of the
Hohenberg--Martin classification of approximations (conserving vs gapless) and
point out that the Popov approximation to the full HFB gives a gapless
single-particle spectrum at all temperatures. The Beliaev second-order
approximation is discussed as the spectrum generated by functional
differentiation of the HFB single--particle Green's function. We emphasize that
the problem of determining the excitation spectrum of a Bose-condensed gas
(homogeneous or inhomogeneous) is difficult because of the need to satisfy
several different constraints.Comment: plain tex, 19 page
Coupled Hartree-Fock-Bogoliubov kinetic equations for a trapped Bose gas
Using the Kadanoff-Baym non-equilibrium Green's function formalism, we derive
the self-consistent Hartree-Fock-Bogoliubov (HFB) collisionless kinetic
equations and the associated equation of motion for the condensate wavefunction
for a trapped Bose-condensed gas. Our work generalizes earlier work by Kane and
Kadanoff (KK) for a uniform Bose gas. We include the off-diagonal (anomalous)
pair correlations, and thus we have to introduce an off-diagonal distribution
function in addition to the normal (diagonal) distribution function. This
results in two coupled kinetic equations. If the off-diagonal distribution
function can be neglected as a higher-order contribution, we obtain the
semi-classical kinetic equation recently used by Zaremba, Griffin and Nikuni
(based on the simpler Popov approximation). We discuss the static local
equilibrium solution of our coupled HFB kinetic equations within the
semi-classical approximation. We also verify that a solution is the rigid
in-phase oscillation of the equilibrium condensate and non-condensate density
profiles, oscillating with the trap frequency.Comment: 25 page
Damped Bogoliubov excitations of a condensate interacting with a static thermal cloud
We calculate the damping of condensate collective excitations at finite
temperatures arising from the lack of equilibrium between the condensate and
thermal atoms. We neglect the non-condensate dynamics by fixing the thermal
cloud in static equilibrium. We derive a set of generalized Bogoliubov
equations for finite temperatures that contain an explicit damping term due to
collisional exchange of atoms between the two components. We have numerically
solved these Bogoliubov equations to obtain the temperature dependence of the
damping of the condensate modes in a harmonic trap. We compare these results
with our recent work based on the Thomas-Fermi approximation.Comment: 9 pages, 3 figures included. Submitted to PR
Quantum Kinetic Theory V: Quantum kinetic master equation for mutual interaction of condensate and noncondensate
A detailed quantum kinetic master equation is developed which couples the
kinetics of a trapped condensate to the vapor of non-condensed particles. This
generalizes previous work which treated the vapor as being undepleted.Comment: RevTeX, 26 pages and 5 eps figure
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
A particle-number-conserving Bogoliubov method which demonstrates the validity of the time-dependent Gross-Pitaevskii equation for a highly condensed Bose gas
The Bogoliubov method for the excitation spectrum of a Bose-condensed gas is
generalized to apply to a gas with an exact large number of particles.
This generalization yields a description of the Schr\"odinger picture field
operators as the product of an annihilation operator for the total number
of particles and the sum of a ``condensate wavefunction'' and a phonon
field operator in the form when the field operator acts on the N particle subspace. It
is then possible to expand the Hamiltonian in decreasing powers of ,
an thus obtain solutions for eigenvalues and eigenstates as an asymptotic
expansion of the same kind. It is also possible to compute all matrix elements
of field operators between states of different N.Comment: RevTeX, 11 page
Does electronic monitoring influence adherence to medication? Randomized controlled trial of measurement reactivity.
BACKGROUND: Electronic monitoring is recommended for accurate measurement of medication adherence but a possible limitation is that it may influence adherence. PURPOSE: To test the reactive effect of electronic monitoring in a randomized controlled trial. METHODS: A total of 226 adults with type 2 diabetes and HbA1c ≥58 mmol/mol were randomized to receiving their main oral glucose lowering medication in electronic containers or standard packaging. The primary outcomes were self-reported adherence measured with the MARS (Medication Adherence Report Scale; range 5-25) and HbA1c at 8 weeks. RESULTS: Non-significantly higher adherence and lower HbA1c were observed in the electronic container group (differences in means, adjusting for baseline value: MARS, 0.4 [95 % CI -0.1 to 0.8, p = 0.11]; HbA1c (mmol/mol), -1.02 [-2.73 to 0.71, p = 0.25]). CONCLUSIONS: Electronic containers may lead to a small increase in adherence but this potential limitation is outweighed by their advantages. Our findings support electronic monitoring as the method of choice in research on medication adherence. (Trial registration Current Controlled Trials ISRCT N30522359)
Dark soliton states of Bose-Einstein condensates in anisotropic traps
Dark soliton states of Bose-Einstein condensates in harmonic traps are
studied both analytically and computationally by the direct solution of the
Gross-Pitaevskii equation in three dimensions. The ground and self-consistent
excited states are found numerically by relaxation in imaginary time. The
energy of a stationary soliton in a harmonic trap is shown to be independent of
density and geometry for large numbers of atoms. Large amplitude field
modulation at a frequency resonant with the energy of a dark soliton is found
to give rise to a state with multiple vortices. The Bogoliubov excitation
spectrum of the soliton state contains complex frequencies, which disappear for
sufficiently small numbers of atoms or large transverse confinement. The
relationship between these complex modes and the snake instability is
investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color
Relaxation rates and collision integrals for Bose-Einstein condensates
Near equilibrium, the rate of relaxation to equilibrium and the transport
properties of excitations (bogolons) in a dilute Bose-Einstein condensate (BEC)
are determined by three collision integrals, ,
, and . All three collision integrals
conserve momentum and energy during bogolon collisions, but only conserves bogolon number. Previous works have considered the
contribution of only two collision integrals, and . In this work, we show that the third collision integral makes a significant contribution to the bogolon number
relaxation rate and needs to be retained when computing relaxation properties
of the BEC. We provide values of relaxation rates in a form that can be applied
to a variety of dilute Bose-Einstein condensates.Comment: 18 pages, 4 figures, accepted by Journal of Low Temperature Physics
7/201
Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps
We study the rotational properties of a Bose-Einstein condensate confined in
a rotating harmonic trap for different trap anisotropies. Using simple
arguments, we derive expressions for the velocity field of the quantum fluid
for condensates with or without vortices. While the condensed gas describes
open spiraling trajectories, on the frame of reference of the rotating trap the
motion of the fluid is against the trap rotation. We also find explicit
formulae for the angular momentum and a linear and Thomas-Fermi solutions for
the state without vortices. In these two limits we also find an analytic
relation between the shape of the cloud and the rotation speed. The predictions
are supported by numerical simulations of the mean field Gross-Pitaevskii
model.Comment: 4 RevTeX pages, 2 EPS figures; typos fixed, reference adde
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