668 research outputs found
Two-component Bose-Einstein Condensates with Large Number of Vortices
We consider the condensate wavefunction of a rapidly rotating two-component
Bose gas with an equal number of particles in each component. If the
interactions between like and unlike species are very similar (as occurs for
two hyperfine states of Rb or Na) we find that the two components
contain identical rectangular vortex lattices, where the unit cell has an
aspect ratio of , and one lattice is displaced to the center of the
unit cell of the other. Our results are based on an exact evaluation of the
vortex lattice energy in the large angular momentum (or quantum Hall) regime.Comment: 4 pages, 2 figures, RevTe
Local Spin-Gauge Symmetry of the Bose-Einstein Condensates in Atomic Gases
The Bose-Einstein condensates of alkali atomic gases are spinor fields with
local ``spin-gauge" symmetry. This symmetry is manifested by a superfluid
velocity (or gauge field) generated by the Berry phase of the
spin field. In ``static" traps, splits the degeneracy of the
harmonic energy levels, breaks the inversion symmetry of the vortex nucleation
frequency , and can lead to {\em vortex ground states}. The
inversion symmetry of , however, is not broken in ``dynamic"
traps. Rotations of the atom cloud can be generated by adiabatic effects
without physically rotating the entire trap.Comment: Typos in the previous version corrected, thanks to the careful
reading of Daniel L. Cox. 13 pages + 2 Figures in uuencode + gzip for
First and Second Sound Modes of a Bose-Einstein Condensate in a Harmonic Trap
We have calculated the first and second sound modes of a dilute interacting
Bose gas in a spherical trap for temperatures () and for
systems with to particles. The second sound modes (which exist
only below ) generally have a stronger temperature dependence than the
first sound modes. The puzzling temperature variations of the sound modes near
recently observed at JILA in systems with particles match
surprisingly well with those of the first and second sound modes of much larger
systems.Comment: a shorten version, more discussions are given on the nature of the
second sound. A long footnote on the recent work of Zaremba, Griffin, and
Nikuni (cond-mat/9705134) is added, the spectrum of the (\ell=1, n_2=0) mode
is included in fig.
Inherent Rheology of a Granular Fluid in Uniform Shear Flow
In contrast to normal fluids, a granular fluid under shear supports a steady
state with uniform temperature and density since the collisional cooling can
compensate locally for viscous heating. It is shown that the hydrodynamic
description of this steady state is inherently non-Newtonian. As a consequence,
the Newtonian shear viscosity cannot be determined from experiments or
simulation of uniform shear flow. For a given degree of inelasticity, the
complete nonlinear dependence of the shear viscosity on the shear rate requires
the analysis of the unsteady hydrodynamic behavior. The relationship to the
Chapman-Enskog method to derive hydrodynamics is clarified using an approximate
Grad's solution of the Boltzmann kinetic equationComment: 10 pages, 4 figures; substantially enlarged version; to be published
in PR
Transport Coefficients for Granular Media from Molecular Dynamics Simulations
Under many conditions, macroscopic grains flow like a fluid; kinetic theory
pred icts continuum equations of motion for this granular fluid. In order to
test the theory, we perform event driven molecular simulations of a
two-dimensional gas of inelastic hard disks, driven by contact with a heat
bath. Even for strong dissipation, high densities, and small numbers of
particles, we find that continuum theory describes the system well. With a bath
that heats the gas homogeneously, strong velocity correlations produce a
slightly smaller energy loss due to inelastic collisions than that predicted by
kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients
are induced. Determination of the resulting fluxes allows calculation of the
thermal conductivity and shear viscosity, which are compared to the predictions
of granular kinetic theory, and which can be used in continuum modeling of
granular flows. The shear viscosity is close to the prediction of kinetic
theory, while the thermal conductivity can be overestimated by a factor of 2;
in each case, transport is lowered with increasing inelasticity.Comment: 14 pages, 17 figures, 39 references, submitted to PRE feb 199
Onset of Patterns in an Ocillated Granular Layer: Continuum and Molecular Dynamics Simulations
We study the onset of patterns in vertically oscillated layers of
frictionless dissipative particles. Using both numerical solutions of continuum
equations to Navier-Stokes order and molecular dynamics (MD) simulations, we
find that standing waves form stripe patterns above a critical acceleration of
the cell. Changing the frequency of oscillation of the cell changes the
wavelength of the resulting pattern; MD and continuum simulations both yield
wavelengths in accord with previous experimental results. The value of the
critical acceleration for ordered standing waves is approximately 10% higher in
molecular dynamics simulations than in the continuum simulations, and the
amplitude of the waves differs significantly between the models. The delay in
the onset of order in molecular dynamics simulations and the amplitude of noise
below this onset are consistent with the presence of fluctuations which are
absent in the continuum theory. The strength of the noise obtained by fit to
Swift-Hohenberg theory is orders of magnitude larger than the thermal noise in
fluid convection experiments, and is comparable to the noise found in
experiments with oscillated granular layers and in recent fluid experiments on
fluids near the critical point. Good agreement is found between the mean field
value of onset from the Swift-Hohenberg fit and the onset in continuum
simulations. Patterns are compared in cells oscillated at two different
frequencies in MD; the layer with larger wavelength patterns has less noise
than the layer with smaller wavelength patterns.Comment: Published in Physical Review
Frequencies and Damping rates of a 2D Deformed Trapped Bose gas above the Critical Temperature
We derive the equation of motion for the velocity fluctuations of a 2D
deformed trapped Bose gas above the critical temperature in the hydrodynamical
regime. From this equation, we calculate the eigenfrequencies for a few
low-lying excitation modes. Using the method of averages, we derive a
dispersion relation in a deformed trap that interpolates between the
collisionless and hydrodynamic regimes. We make use of this dispersion relation
to calculate the frequencies and the damping rates for monopole and quadrupole
mode in both the regimes. We also discuss the time evolution of the wave packet
width of a Bose gas in a time dependent as well as time independent trap.Comment: 13 pages, latex fil
Stability and collective excitations of a two-component Bose-condensed gas: a moment approach
The dynamics of a two-component dilute Bose gas of atoms at zero temperature
is described in the mean field approximation by a two-component
Gross-Pitaevskii Equation. We solve this equation assuming a Gaussian shape for
the wavefunction, where the free parameters of the trial wavefunction are
determined using a moment method. We derive equilibrium states and the phase
diagrams for the stability for positive and negative s-wave scattering lengths,
and obtain the low energy excitation frequencies corresponding to the
collective motion of the two Bose condensates.Comment: 7 pages, 6 figure
Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases
It is shown that the hydrodynamic modes of a dilute granular gas of inelastic
hard spheres can be identified, and calculated in the long wavelength limit.
Assuming they dominate at long times, formal expressions for the Navier-Stokes
transport coefficients are derived. They can be expressed in a form that
generalizes the Green-Kubo relations for molecular systems, and it is shown
that they can also be evaluated by means of -particle simulation methods.
The form of the hydrodynamic modes to zeroth order in the gradients is used to
detect the presence of inherent velocity correlations in the homogeneous
cooling state, even in the low density limit. They manifest themselves in the
fluctuations of the total energy of the system. The theoretical predictions are
shown to be in agreement with molecular dynamics simulations. Relevant related
questions deserving further attention are pointed out
Societal emotional environments and cross-cultural differences in life satisfaction: A forty-nine country study
In this paper, we introduce the concept of ‘societal emotional environment’: the emotional climate of a society (operationalized as the degree to which positive and negative emotions are expressed in a society). Using data collected from 12,888 participants across 49 countries, we show how societal emotional environments vary across countries and cultural clusters, and we consider the potential importance of these differences for well-being. Multilevel analyses supported a ‘double-edged sword’ model of negative emotion expression, where expression of negative emotions predicted higher life satisfaction for the expresser but lower life satisfaction for society. In contrast, partial support was found for higher societal life satisfaction in positive societal emotional environments. Our study highlights the potential utility and importance of distinguishing between positive and negative emotion expression, and adopting both individual and societal perspectives in well-being research. Individual pathways to happiness may not necessarily promote the happiness of others.info:eu-repo/semantics/publishedVersio
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