27 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
Stability of Bose condensed atomic Li-7
We study the stability of a Bose condensate of atomic Li in a (harmonic
oscillator) magnetic trap at non-zero temperatures. In analogy to the stability
criterion for a neutron star, we conjecture that the gas becomes unstable if
the free energy as a function of the central density of the cloud has a local
extremum which conserves the number of particles. Moreover, we show that the
number of condensate particles at the point of instability decreases with
increasing temperature, and that for the temperature interval considered, the
normal part of the gas is stable against density fluctuations at this point.Comment: Submitted for publication in Physical Review
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
Split-merge cycle, fragmented collapse, and vortex disintegration in rotating Bose-Einstein condensates with attractive interactions
The dynamical instabilities and ensuing dynamics of singly- and
doubly-quantized vortex states of Bose-Einstein condensates with attractive
interactions are investigated using full 3D numerical simulations of the
Gross-Pitaevskii equation. With increasing the strength of attractive
interactions, a series of dynamical instabilities such as quadrupole, dipole,
octupole, and monopole instabilities emerge. The most prominent instability
depends on the strength of interactions, the geometry of the trapping
potential, and deviations from the axisymmetry due to external perturbations.
Singly-quantized vortices split into two clusters and subsequently undergo
split-merge cycles in a pancake-shaped trap, whereas the split fragments
immediately collapse in a spherical trap. Doubly-quantized vortices are always
unstable to disintegration of the vortex core. If we suddenly change the
strength of interaction to within a certain range, the vortex splits into three
clusters, and one of the clusters collapses after a few split-merge cycles. The
vortex split can be observed using a current experimental setup of the MIT
group.Comment: 11 pages, 10 figure
Stability of trapped Bose-Einstein condensates
In three-dimensional trapped Bose-Einstein condensate (BEC), described by the
time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of
initial conditions on stability using a Gaussian variational approach and exact
numerical simulations. We also discuss the validity of the criterion for
stability suggested by Vakhitov and Kolokolov. The maximum initial chirp
(initial focusing defocusing of cloud) that can lead a stable condensate to
collapse even before the number of atoms reaches its critical limit is obtained
for several specific cases. When we consider two- and three-body nonlinear
terms, with negative cubic and positive quintic terms, we have the conditions
for the existence of two phases in the condensate. In this case, the magnitude
of the oscillations between the two phases are studied considering sufficient
large initial chirps. The occurrence of collapse in a BEC with repulsive
two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure
Resonant Generation of Topological Modes in Trapped Bose Gases
Trapped Bose atoms cooled down to temperatures below the Bose-Einstein
condensation temperature are considered. Stationary solutions to the
Gross-Pitaevskii equation (GPE) define the topological coherent modes,
representing nonground-state Bose-Einstein condensates. These modes can be
generated by means of alternating fields whose frequencies are in resonance
with the transition frequencies between two collective energy levels
corresponding to two different topological modes. The theory of resonant
generation of these modes is generalized in several aspects: Multiple-mode
formation is described; a shape-conservation criterion is derived, imposing
restrictions on the admissible spatial dependence of resonant fields; evolution
equations for the case of three coherent modes are investigated; the complete
stability analysis is accomplished; the effects of harmonic generation and
parametric conversion for the topological coherent modes are predicted. All
considerations are realized both by employing approximate analytical methods as
well as by numerically solving the GPE. Numerical solutions confirm all
conclusions following from analytical methods.Comment: One reference modifie
Bose condensates in a harmonic trap near the critical temperature
The mean-field properties of finite-temperature Bose-Einstein gases confined
in spherically symmetric harmonic traps are surveyed numerically. The solutions
of the Gross-Pitaevskii (GP) and Hartree-Fock-Bogoliubov (HFB) equations for
the condensate and low-lying quasiparticle excitations are calculated
self-consistently using the discrete variable representation, while the most
high-lying states are obtained with a local density approximation. Consistency
of the theory for temperatures through the Bose condensation point requires
that the thermodynamic chemical potential differ from the eigenvalue of the GP
equation; the appropriate modifications lead to results that are continuous as
a function of the particle interactions. The HFB equations are made gapless
either by invoking the Popov approximation or by renormalizing the particle
interactions. The latter approach effectively reduces the strength of the
effective scattering length, increases the number of condensate atoms at each
temperature, and raises the value of the transition temperature relative to the
Popov approximation. The renormalization effect increases approximately with
the log of the atom number, and is most pronounced at temperatures near the
transition. Comparisons with the results of quantum Monte Carlo calculations
and various local density approximations are presented, and experimental
consequences are discussed.Comment: 15 pages, 11 embedded figures, revte
Quantum Kinetic Theory III: Quantum kinetic master equation for strongly condensed trapped systems
We extend quantum kinetic theory to deal with a strongly Bose-condensed
atomic vapor in a trap. The method assumes that the majority of the vapor is
not condensed, and acts as a bath of heat and atoms for the condensate. The
condensate is described by the particle number conserving Bogoliubov method
developed by one of the authors. We derive equations which describe the
fluctuations of particle number and phase, and the growth of the Bose-Einstein
condensate. The equilibrium state of the condensate is a mixture of states with
different numbers of particles and quasiparticles. It is not a quantum
superposition of states with different numbers of particles---nevertheless, the
stationary state exhibits the property of off-diagonal long range order, to the
extent that this concept makes sense in a tightly trapped condensate.Comment: 3 figures submitted to Physical Review
Factors associated with depressive mood at the onset of multiple sclerosis - an analysis of 781 patients of the German NationMS cohort
BACKGROUND: Depression has a major impact on the disease burden of multiple sclerosis (MS). Analyses of overlapping MS and depression risk factors [smoking, vitamin D (25-OH-VD) and Epstein-Barr virus (EBV) infection] and sex, age, disease characteristics and neuroimaging features associated with depressive symptoms in early MS are scarce. OBJECTIVES: To assess an association of MS risk factors with depressive symptoms within the German NationMS cohort. DESIGN: Cross-sectional analysis within a multicenter observational study. METHODS: Baseline data of n = 781 adults with newly diagnosed clinically isolated syndrome or relapsing-remitting MS qualified for analysis. Global and region-specific magnetic resonance imaging (MRI)-volumetry parameters were available for n = 327 patients. Association of demographic factors, MS characteristics and risk factors [sex, age, smoking, disease course, presence of current relapse, expanded disability status scale (EDSS) score, fatigue (fatigue scale motor cognition), 25-OH-VD serum concentration, EBV nuclear antigen-1 IgG (EBNA1-IgG) serum levels] and depressive symptoms (Beck Depression Inventory-II, BDI-II) was tested as a primary outcome by multivariable linear regression. Non-parametric correlation and group comparison were performed for associations of MRI parameters and depressive symptoms. RESULTS: Mean age was 34.3 years (95% confidence interval: 33.6-35.0). The female-to-male ratio was 2.3:1. At least minimal depressive symptoms (BDI-II > 8) were present in n = 256 (32.8%), 25-OH-VD deficiency (<20 ng/ml) in n = 398 (51.0%), n = 246 (31.5%) participants were smokers. Presence of current relapse [coefficient (c) = 1.48, p = 0.016], more severe fatigue (c = 0.26, p < 0.0001), lower 25-OH-VD (c = -0.03, p = 0.034) and smoking (c = 0.35, p = 0.008) were associated with higher BDI-II scores. Sex, age, disease course, EDSS, month of visit, EBNA1-IgG levels and brain volumes at baseline were not. CONCLUSION: Depressive symptoms need to be assessed in early MS. Patients during relapse seem especially vulnerable to depressive symptoms. Contributing factors such as fatigue, vitamin D deficiency and smoking, could specifically be targeted in future interventions and should be investigated in prospective studies