Vortex stabilization in a small rotating asymmetric Bose-Einstein condensate

We use a variational method to investigate the ground-state phase diagram of a small, asymmetric Bose-Einstein condensate with respect to the dimensionless interparticle interaction strength $\gamma$ and the applied external rotation speed $\Omega$. For a given $\gamma$, the transition lines between no-vortex and vortex states are shifted toward higher $\Omega$ relative to those for the symmetric case. We also find a re-entrant behavior, where the number of vortex cores can decrease for large $\Omega$. In addition, stabilizing a vortex in a rotating asymmetric trap requires a minimum interaction strength. For a given asymmetry, the evolution of the variational parameters with increasing $\Omega$ shows two different types of transitions (sharp or continuous), depending on the strength of the interaction. We also investigate transitions to states with higher vorticity; the corresponding angular momentum increases continuously as a function of $\Omega$

Stability of rotating states in a weakly-interacting Bose-Einstein condensate

We investigate the lowest state of a rotating, weakly-interacting Bose-Einstein condensate trapped in a harmonic confining potential that is driven by an infinitesimally asymmetric perturbation. Although in an axially-symmetric confining potential the gas has an axially-symmetric single-particle density distribution, we show that in the presence of the small asymmetric perturbation its lowest state is the one given by the mean-field approximation, which is a broken-symmetric state. We also estimate the rate of relaxation of angular momentum when the gas is no longer driven by the asymmetric perturbation and identify two regimes of "slow" and "fast" relaxation. States of certain symmetry are found to be more robust.Comment: 6 pages, RevTe

Reactions to uncertainty and the accuracy of diagnostic mammography.

BackgroundReactions to uncertainty in clinical medicine can affect decision making.ObjectiveTo assess the extent to which radiologists' reactions to uncertainty influence diagnostic mammography interpretation.DesignCross-sectional responses to a mailed survey assessed reactions to uncertainty using a well-validated instrument. Responses were linked to radiologists' diagnostic mammography interpretive performance obtained from three regional mammography registries.ParticipantsOne hundred thirty-two radiologists from New Hampshire, Colorado, and Washington.MeasurementMean scores and either standard errors or confidence intervals were used to assess physicians' reactions to uncertainty. Multivariable logistic regression models were fit via generalized estimating equations to assess the impact of uncertainty on diagnostic mammography interpretive performance while adjusting for potential confounders.ResultsWhen examining radiologists' interpretation of additional diagnostic mammograms (those after screening mammograms that detected abnormalities), a 5-point increase in the reactions to uncertainty score was associated with a 17% higher odds of having a positive mammogram given cancer was diagnosed during follow-up (sensitivity), a 6% lower odds of a negative mammogram given no cancer (specificity), a 4% lower odds (not significant) of a cancer diagnosis given a positive mammogram (positive predictive value [PPV]), and a 5% higher odds of having a positive mammogram (abnormal interpretation).ConclusionMammograms interpreted by radiologists who have more discomfort with uncertainty have higher likelihood of being recalled

Weakly Interacting Bose-Einstein Condensates Under Rotation: Mean-field versus Exact Solutions

We consider a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation and investigate the connection between the energies obtained from mean-field calculations and from exact diagonalizations in a subspace of degenerate states. From the latter we derive an approximation scheme valid in the thermodynamic limit of many particles. Mean-field results are shown to emerge as the correct leading-order approximation to exact calculations in the same subspace.Comment: 4 pages, RevTex, submitted to PR

Stability of small amplitude normal modes of a Bose-Einstein condensate with a singly quantized vortex confined in an optical lattice

We study the dynamics of a BEC with a singly quantized vortex, placed in the combined potential of a 1-D (2-D) optical lattice and an axi-symmetric harmonic trap. A time-dependent variational Lagrangian analysis shows that an optical lattice helps to stabilize the vortex which in absence of the optical lattice is unstable. We find that the normal modes are stable only if the depth of the optical potential is more than a certain critical value. This critical value of the optical potential depends on the interaction parameter.In general higher the interaction parameter,lower the value of the optical potential required to stabilize the vortex. The BEC with the singly quantized vortex is found to be relatively more unstable in a 2-D optical lattice compared to a 1-D optical lattice.Comment: Revised version with 11 pages including 1 figur

The Ellipticity and Orientation of Clusters of Galaxies from N-Body Experiments

In this study we use simulations of 128$^3$ particles to study the ellipticity and orientation of clusters of galaxies in N-body simulations of differing power-law initial spectra (P(k) \propto k^n ,n = +1, 0, -1, -2$), and density parameters ($\Omega_0 = 0.2$to 1.0). Furthermore, unlike most theoretical studies we mimic most observers by removing all particles which lie at distances greater than 2 1/h Mpc from the cluster center of mass. We computed the axial ratio and the principal axes using the inertia tensor of each cluster. The mean ellipticity of clusters increases strongly with increasing$n$. We also find that clusters tend to become more spherical at smaller radii. We compared the orientation of a cluster to the orientation of neighboring clusters as a function of distance (correlation). In addition, we considered whether a cluster's major axis tends to lie along the line connecting it to a neighboring cluster, as a function of distance (alignment). Both alignments and correlations were computed in three dimensions and in projection to mimic observational surveys. Our results show that significant alignments exist for all spectra at small separations ($D < 15 h^{-1}$Mpc) but drops off at larger distance in a strongly$n-$dependent way.Comment: 22 pages, requires aaspp4.sty, flushrt.sty, and epsf.sty Revised manuscript, accepted for publication in Ap

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