785 research outputs found
The Yrast Spectra of Weakly Interacting Bose-Einstein Condensates
The low energy quantal spectrum is considered as a function of the total
angular momentum for a system of weakly interacting bosonic atoms held together
by an external isotropic harmonic potential. It is found that besides the usual
condensation into the lowest state of the oscillator, the system exhibits two
additional kinds of condensate and associated thermodynamic phase transitions.
These new phenomena are derived from the degrees of freedom of "partition
space" which describes the multitude of different ways in which the angular
momentum can be distributed among the atoms while remaining all the time in the
lowest state of the oscillator
A Relational Event Approach to Modeling Behavioral Dynamics
This chapter provides an introduction to the analysis of relational event
data (i.e., actions, interactions, or other events involving multiple actors
that occur over time) within the R/statnet platform. We begin by reviewing the
basics of relational event modeling, with an emphasis on models with piecewise
constant hazards. We then discuss estimation for dyadic and more general
relational event models using the relevent package, with an emphasis on
hands-on applications of the methods and interpretation of results. Statnet is
a collection of packages for the R statistical computing system that supports
the representation, manipulation, visualization, modeling, simulation, and
analysis of relational data. Statnet packages are contributed by a team of
volunteer developers, and are made freely available under the GNU Public
License. These packages are written for the R statistical computing
environment, and can be used with any computing platform that supports R
(including Windows, Linux, and Mac).
Plant species roles in pollination networks: an experimental approach
Pollination is an important ecosystem service threatened by current pollinator declines, making flower planting schemes an important strategy to recover pollination function. However, ecologists rarely test the attractiveness of chosen plants to pollinators in the field. Here, we experimentally test whether plant species roles in pollination networks can be used to identify species with the most potential to recover plant–pollinator communities. Using published pollination networks, we calculated each plant's centrality and chose five central and five peripheral plant species for introduction into replicate experimental plots. Flower visitation by pollinators was recorded in each plot and we tested the impact of introduced central and peripheral plant species on the pollinator and resident plant communities and on network structure. We found that the introduction of central plant species attracted a higher richness and abundance of pollinators than the introduction of peripheral species, and that the introduced central plant species occupied the most important network roles. The high attractiveness of central species to pollinators, however, did not negatively affect visitation to resident plant species by pollinators. We also found that the introduction of central plant species did not affect network structure, while networks with introduced peripheral species had lower centralisation and interaction evenness than networks with introduced central species. To our knowledge, this is the first time species network roles have been tested in a field experiment. Given that most restoration projects start at the plant community, being able to identify the plants with the highest potential to restore community structure and functioning should be a key goal for ecological restoration
Rotating Bose gas with hard-core repulsion in a quasi-2D harmonic trap: vortices in BEC
We consider a gas of N(=6, 10, 15) Bose particles with hard-core repulsion,
contained in a quasi-2D harmonic trap and subjected to an overall angular
velocity about the z-axis. Exact diagonalization of the
many-body Hamiltonian matrix in given subspaces of the total (quantized)
angular momentum L, with (e.g. for L=N=15, n =240782)
was carried out using Davidson's algorithm. The many-body variational ground
state wavefunction, as also the corresponding energy and the reduced
one-particle density-matrix were calculated. With the usual identification of
as the Lagrange multiplier associated with L for a rotating
system, the phase diagram (or the stability line) was determined
that gave a number of critical angular velocities at which the ground state angular momentum and the associated
condensate fraction undergo abrupt jumps.
A number of (total) angular momentum states were found to be stable at
successively higher critical angular velocities $\Omega_{{\bf c}i}, \
i=1,2,3,...L_{z}>N\Omega_{{\bf c}i}_{z}(\sim 4)$ orders of magnitude in the moderately to the weakly
interacting regime.Comment: Revtex, 11 pages, 1 table as ps file, 4 figures as ps file
Fermi-Bose quantum degenerate ^40 K - ^87 Rb mixture with attractive interaction
We report on the achievement of simultaneous quantum degeneracy in a mixed
gas of fermionic ^40 K and bosonic ^87 Rb. Potassium is cooled to 0.3 times the
Fermi temperature by means of an efficient thermalization with evaporatively
cooled rubidium. Direct measurement of the collisional cross-section confirms a
large interspecies attraction. This interaction is shown to affect the
expansion of the Bose-Einstein condensate released form the magnetic trap,
where it is immersed in the Fermi sea.Comment: 5 pages, 4 figures, replaced one figure plus some change
Phase diagram of quantized vortices in a trapped Bose-Einstein condensed gas
We investigate the thermodynamic stability of quantized vortices in a dilute
Bose gas confined by a rotating harmonic trap at finite temperature.
Interatomic forces play a crucial role in characterizing the resulting phase
diagram, especially in the large Thomas-Fermi regime. We show that the
critical temperature for the creation of stable vortices exhibits a maximum as
a function of the frequency of the rotating trap and that the corresponding
transition is associated with a discontinuity in the number of atoms in the
condensate. Possible strategies for approaching the vortical region are
discussed.Comment: Revtex, 4 pages, 2 figure
Correlations in a Confined gas of Harmonically Interacting Spin-Polarized Fermions
For a fermion gas with equally spaced energy levels, the density and the pair
correlation function are obtained. The derivation is based on the path integral
approach for identical particles and the inversion of the generating functions
for both static responses. The density and the pair correlation function are
evaluated explicitly in the ground state of a confined fermion system with a
number of particles ranging from 1 to 220 and filling the Fermi level
completely.Comment: 11 REVTEX pages, 3 postscript figures. Accepted for publication in
Phys. Rev. E, Vol. 58 (August 1, 1998
Coherent Dynamics of Vortex Formation in Trapped Bose-Einstein Condensates
Simulations of a rotationally stirred condensate show that a regime of simple
behaviour occurs in which a single vortex cycles in and out of the condensate.
We present a simple quantitative model of this behaviour, which accurately
describes the full vortex dynamics, including a critical angular speed of
stirring for vortex formation. A method for experimentally preparing a
condensate in a central vortex state is suggested.Comment: 4 pages, 4 figures, REVTeX 3.1; Submitted to Physical Review Letters
(5 February 1999); See http://www.physics.otago.ac.nz/research/bec/vortex for
MPEG movies and further information; Accepted for Physical Review Letters (24
June 1999); Changes: updated Figs 1 and 2 (new style), minor typos fixed,
more discussion at en
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
Analytical results for a trapped, weakly-interacting Bose-Einstein condensate under rotation
We examine the problem of a repulsive, weakly-interacting and harmonically
trapped Bose-Einstein condensate under rotation. We derive a simple analytic
expression for the energy incorporating the interactions when the angular
momentum per particle is between zero and one and find that the interaction
energy decreases linearly as a function of the angular momentum in agreement
with previous numerical and limiting analytical studies.Comment: 3 pages, RevTe
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