1,716 research outputs found
Radial and angular rotons in trapped dipolar gases
We study Bose-Einstein condensates with purely dipolar interactions in oblate
(pancake) traps. We find that the condensate always becomes unstable to
collapse when the number of particles is sufficiently large. We analyze the
instability, and find that it is the trapped-gas analogue of the
``roton-maxon'' instability previously reported for a gas that is unconfined in
two dimensions. In addition, we find that under certain circumstances, the
condensate wave function attains a biconcave shape, with its maximum density
away from the center of the gas. These biconcave condensates become unstable
due to azimuthl excitation - an angular roton.Comment: 4 pages, 3 figure
Fundamental domains and generators for lattice Veech groups
The moduli space QMg of non-zero genus g quadratic differentials has a natural action of G=GL+2(R) / ⟨±(1001) ⟩. The Veech group PSL(X,q) is the stabilizer of (X,q)∈QMg in G. We describe a new algorithm for finding elements of PSL(X,q) which, for lattice Veech groups, can be used to compute a fundamental domain and generators. Using our algorithm, we give the first explicit examples of generators and fundamental domains for non-arithmetic Veech groups where the genus of H / PSL(X,q) is greater than zero
Dynamical pattern formation during growth of a dual-species Bose-Einstein condensate
We simulate the growth of a dual species Bose-Einstein condensate using a
Gross-Pitaevskii equation with an additional gain term giving rise to the
growth. Such growth occurs during simultaneous evaporative cooling of a mixture
of two gases. The ground state of a dual condensate is normally either a
miscible mixture, or an immiscible phase with two spatially separated
components. In a cigar trap the ground state typically consists of one
component in the center, and the other component flanking it. Our simulations
show that when the condensates are formed in a cigar trap and the mixture is
phase separated, then the final state upon the end of the growth is generally
far from the true ground state of the system. Instead it consists of multiple,
interleaved bubbles of the two species. Such a pattern was observed recently in
an experiment by Wieman's group at JILA, and our simulations are in good
qualitative agreement with the experiment. We explain the pattern formation as
due to the onset of modulation instability during growth, and study the
dependence of the final state pattern on various parameters of the system
Dipolar Bose gases: Many-body versus mean-field description
We characterize zero-temperature dipolar Bose gases under external spherical
confinement as a function of the dipole strength using the essentially exact
many-body diffusion Monte Carlo (DMC) technique. We show that the DMC energies
are reproduced accurately within a mean-field framework if the variation of the
s-wave scattering length with the dipole strength is accounted for properly.
Our calculations suggest stability diagrams and collapse mechanisms of dipolar
Bose gases that differ significantly from those previously proposed in the
literature
An efficiency upper bound for inverse covariance estimation
We derive an upper bound for the efficiency of estimating entries in the
inverse covariance matrix of a high dimensional distribution. We show that in
order to approximate an off-diagonal entry of the density matrix of a
-dimensional Gaussian random vector, one needs at least a number of samples
proportional to . Furthermore, we show that with samples, the
hypothesis that two given coordinates are fully correlated, when all other
coordinates are conditioned to be zero, cannot be told apart from the
hypothesis that the two are uncorrelated.Comment: 7 Page
Implications of the Babinet Principle for Casimir Interactions
We formulate the Babinet Principle (BP) as a relation between the scattering
amplitudes for electromagnetic waves, and combine it with multiple scattering
techniques to derive new properties of Casimir forces. We show that the Casimir
force exerted by a planar conductor or dielectric on a self- complementary
perforated planar mirror is approximately half that on a uniform mirror
independent of the distance between them. The BP suggests that Casimir edge
effects are anomalously small, supporting results obtained earlier in special
cases. Finally, we illustrate how the BP can be used to estimate Casimir forces
between perforated planar mirrors
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