Spatial fragmentation of a Bose-Einstein condensate in a double-well potential

We present a theoretical study of the ground state of a Bose-Einstein condensate with repulsive inter-particle interactions in a double-well potential, using a restricted variational principle. Within such an approach, there is a transition from a single condensate to a fragmented condensate as the strength of the central barrier of the potential is increased. We determine the nature of this transition through approximate analytic as well as numerical solutions of our model in the regime where the inter-particle interactions can be treated perturbatively. The degree of fragmentation of the condensate is characterized by the degrees of first-order and second-order spatial coherence across the barrier.Comment: 10 pages, 2 figures, submitted to Phys. Rev.

Quantum Phases of Vortices in Rotating Bose-Einstein Condensates

We investigate the groundstates of weakly interacting bosons in a rotating trap as a function of the number of bosons, $N$, and the average number of vortices, $N_V$. We identify the filling fraction $\nu\equiv N/N_V$ as the parameter controlling the nature of these states. We present results indicating that, as a function of $\nu$, there is a zero temperature {\it phase transition} between a triangular vortex lattice phase, and strongly-correlated vortex liquid phases. The vortex liquid phases appear to be the Read-Rezayi parafermion states

Study protocol for improving asthma outcomes through cross-cultural communication training for physicians: a randomized trial of physician training

Abstract Background Massive resources are expended every year on cross-cultural communication training for physicians. Such training is a focus of continuing medical education nationwide and is part of the curriculum of virtually every medical school in America. There is a pressing need for evidence regarding the effects on patients of cross-cultural communication training for physicians. There is a need to understand the added benefit of such training compared to more general communication. We know of no rigorous study that has assessed whether cross-cultural communication training for physicians results in better health outcomes for their patients. The current study aims to answer this question by enhancing the Physician Asthma Care Education (PACE) program to cross cultural communication (PACE Plus), and comparing the effect of the enhanced program to PACE on the health outcomes of African American and Latino/Hispanic children with asthma. Methods/Design A three-arm randomized control trial is used to compare PACE Plus, PACE, and usual care. Both PACE and PACE Plus are delivered in two, two-hour sessions over a period of two weeks to 5–10 primary care physicians who treat African American and Latino/Hispanic children with asthma. One hundred twelve physicians and 1060 of their pediatric patients were recruited who self-identify as African American or Latino/Hispanic and experience persistent asthma. Physicians were randomized into receiving either the PACE Plus or PACE intervention or into the control group. The comparative effectiveness of PACE and PACE Plus on clinician’s therapeutic and communication practices with the family/patient, children’s urgent care use for asthma, asthma control, and quality of life, and parent/caretaker satisfaction with physician performance will be assessed. Data are collected via telephone survey and medical record review at baseline, 9 months following the intervention, and 21 months following the intervention. Discussion This study aims to reduce disparities in asthma outcomes among African American and Latino/Hispanic children through cross-cultural communication training of their physicians and assessing the added value of this training compared to general communication. The results of this study will provide important information about the value of cross-cultural training in helping to address persistent racial disparities in outcomes. Trial registration ClinicalTrials.gov: NCT01251523 December 1, 2010http://deepblue.lib.umich.edu/bitstream/2027.42/109533/1/12909_2014_Article_948.pd

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

We study the rotational properties of an attractively interacting Bose gas in a quadratic + quartic potential. The low-lying modes of both rotational ground state configurations, namely the vortex and the center of mass rotating states, are solved. The vortex excitation spectrum is positive for weak interactions but the lowest modes decrease rapidly to negative values when the interactions become stronger. The broken rotational symmetry involved in the center of mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center of mass rotational state also demonstrate the coupling between the center of mass and relative motions.Comment: 4 pages, 3 eps figures (2 in color) v2: changes in Title, all figures, in text (especially in Sec III) and in Reference

Topological Defects in the Abrikosov Lattice of Vortices in Type-II Superconductors

The free energy costs for various defects within an Abrikosov lattice of vortices are calculated using the lowest Landau level approximation (LLL). Defect solutions with boundary conditions for lines to meet at a point (crossing defect) and for lines to twist around each other (braid defect) are sought for 2, 3, 6, and 12 lines. Many results have been unexpected, including the nonexistence of a stable two- or three-line braid. This, and the high energy cost found for a six-line braid lead us to propose that the equilibrium vortex state is not entangled below the irreversibility line of the high-$T_c$ superconductors or in a large part of the vortex-liquid phase above this line. Also, the solution for an infinite straight screw dislocation is found, and used to give a limiting form for the free energy cost of very large braids. This depends on the area enclosed by the braid as well as its perimeter length.Comment: 30 pages, 17 Encapsulated PostScript figures, uses Revtex (with epsf

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 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

Morse theory of the moment map for representations of quivers

The results of this paper concern the Morse theory of the norm-square of the moment map on the space of representations of a quiver. We show that the gradient flow of this function converges, and that the Morse stratification induced by the gradient flow co-incides with the Harder-Narasimhan stratification from algebraic geometry. Moreover, the limit of the gradient flow is isomorphic to the graded object of the Harder-Narasimhan-Jordan-H\"older filtration associated to the initial conditions for the flow. With a view towards applications to Nakajima quiver varieties we construct explicit local co-ordinates around the Morse strata and (under a technical hypothesis on the stability parameter) describe the negative normal space to the critical sets. Finally, we observe that the usual Kirwan surjectivity theorems in rational cohomology and integral K-theory carry over to this non-compact setting, and that these theorems generalize to certain equivariant contexts.Comment: 48 pages, small revisions from previous version based on referee's comments. To appear in Geometriae Dedicat

Trapped Protostellar Winds and their Breakout

Observations show that high-velocity jets stem from deeply embedded young stars, which may still be experiencing infall from their parent cloud cores. Yet theory predicts that, early in this buildup, any outgoing wind is trapped by incoming material of low angular momentum. As collapse continues and brings in more rapidly rotating gas, the wind can eventually break out. Here we model this transition by following the motion of the shocked shell created by impact of the wind and a rotating, collapsing envelope. We first demonstrate, both analytically and numerically, that our previous, quasi-static solutions are dynamically unstable. Our present, fully time-dependent calculations include cases both where the wind is driven back by infall to the stellar surface, and where it erupts as a true outflow. For the latter, we find that the time of breakout is sim 50,000 yr for wind speeds of 200 km/s. The reason for the delay is that the shocked material, including the swept-up infall, must be able to climb out of the star's gravitational potential well. We explore the critical wind speed necessary for breakout as a function of the mass transport rates in the wind and infall, as well as the cloud rotation rate Omega0 and time since the start of infall. Breakout does occur for realistic parameter choices. The actual breakout times would change if we relaxed the assumption of perfect mixing between the wind and infall material. Our expanding shells do not exhibit the collimation of observed jets, but continue to expand laterally. To halt this expansion, the density in the envelope must fall off less steeply than in our model.Comment: 44 pages, 10 figures, accepted to Ap

Cross section and analyzing power of pol{p}p -> pn pi+ near threshold

The cross section and analyzing power of the pol{p}p -> pn pi+ reaction near threshold are estimated in terms of data obtained from the pol{p}p -> d pi+ and pp -> pp pi0 reactions. A simple final state interaction theory is developed which depends weakly upon the form of the pion-production operator and includes some Coulomb corrections. Within the uncertainties of the model and the input data, the approach reproduces well the measured energy dependence of the total cross section and the proton analyzing power at a fixed pion c.m. angle of 90deg, from threshold to T_p = 330 MeV. The variation of the differential cross section with pion angle is also very encouraging.Comment: 20 pages, Latex including 4 eps figure