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 ${\bf u}_{s}$ (or gauge field) generated by the Berry phase of the spin field. In ``static" traps, ${\bf u}_{s}$ splits the degeneracy of the harmonic energy levels, breaks the inversion symmetry of the vortex nucleation frequency ${\bf \Omega}_{c1}$, and can lead to {\em vortex ground states}. The inversion symmetry of ${\bf \Omega}_{c1}$, 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

Variational study of a dilute Bose condensate in a harmonic trap

A two-parameter trial condensate wave function is used to find an approximate variational solution to the Gross-Pitaevskii equation for $N_0$ condensed bosons in an isotropic harmonic trap with oscillator length $d_0$ and interacting through a repulsive two-body scattering length $a>0$. The dimensionless parameter ${\cal N}_0 \equiv N_0a/d_0$ characterizes the effect of the interparticle interactions, with ${\cal N}_0 \ll 1$ for an ideal gas and ${\cal N}_0 \gg 1$ for a strongly interacting system (the Thomas-Fermi limit). The trial function interpolates smoothly between these two limits, and the three separate contributions (kinetic energy, trap potential energy, and two-body interaction energy) to the variational condensate energy and the condensate chemical potential are determined parametrically for any value of ${\cal N}_0$, along with illustrative numerical values. The straightforward generalization to an anisotropic harmonic trap is considered briefly.Comment: 14 pages, RevTeX, submitted to Journal of Low Temperature Physic

Transfer Entropy Estimation and Directional Coupling Change Detection in Biomedical Time Series

Background: The detection of change in magnitude of directional coupling between two non-linear time series is a common subject of interest in the biomedical domain, including studies involving the respiratory chemoreflex system. Although transfer entropy is a useful tool in this avenue, no study to date has investigated how different transfer entropy estimation methods perform in typical biomedical applications featuring small sample size and presence of outliers. Methods: With respect to detection of increased coupling strength, we compared three transfer entropy estimation techniques using both simulated time series and respiratory recordings from lambs. The following estimation methods were analyzed: fixed-binning with ranking, kernel density estimation (KDE), and the Darbellay-Vajda (D-V) adaptive partitioning algorithm extended to three dimensions. In the simulated experiment, sample size was varied from 50 to 200, while coupling strength was increased. In order to introduce outliers, the heavy-tailed Laplace distribution was utilized. In the lamb experiment, the objective was to detect increased respiratoryrelated chemosensitivity to O[subscript 2] and CO[subscript 2] induced by a drug, domperidone. Specifically, the separate influence of end-tidal PO[subscript 2] and PCO[subscript 2] on minute ventilation ([dot over V][subscript E]) before and after administration of domperidone was analyzed. Results: In the simulation, KDE detected increased coupling strength at the lowest SNR among the three methods. In the lamb experiment, D-V partitioning resulted in the statistically strongest increase in transfer entropy post-domperidone for PO2 → [dot over V][subscript E]. In addition, D-V partitioning was the only method that could detect an increase in transfer entropy for PCO[subscript 2] → [dot over V][subscript E], in agreement with experimental findings. Conclusions: Transfer entropy is capable of detecting directional coupling changes in non-linear biomedical time series analysis featuring a small number of observations and presence of outliers. The results of this study suggest that fixed-binning, even with ranking, is too primitive, and although there is no clear winner between KDE and D-V partitioning, the reader should note that KDE requires more computational time and extensive parameter selection than D-V partitioning. We hope this study provides a guideline for selection of an appropriate transfer entropy estimation method.National Institutes of Health (U.S.) (Grant R01-EB001659)National Institutes of Health (U.S.) (Grant R01- HL73146)National Institutes of Health (U.S.) (Grant HL085188-01A2)National Institutes of Health (U.S.) (Grant HL090897-01A2)National Institutes of Health (U.S.) (Grant K24 HL093218-01A1)National Institutes of Health (U.S.) (Cooperative Agreement U01-EB-008577)National Institutes of Health (U.S.) (Training Grant T32-HL07901))American Heart Association (Grant 0840159N

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.Comment: 6 pages, 5 figures, submitted to Physical Review

Order Parameter at the Boundary of a Trapped Bose Gas

Through a suitable expansion of the Gross-Pitaevskii equation near the classical turning point, we obtain an explicit solution for the order parameter at the boundary of a trapped Bose gas interacting with repulsive forces. The kinetic energy of the system, in terms of the classical radius $R$ and of the harmonic oscillator length $a_{_{HO}}$, follows the law $E_{kin}/N \propto R^{-2} [\log (R/a_{_{HO}}) + \hbox{const.}]$, approaching, for large $R$, the results obtained by solving numerically the Gross-Pitaevskii equation. The occurrence of a Josephson-type current in the presence of a double trap potential is finally discussed.Comment: 11 pages, REVTEX, 4 figures (uuencoded-gzipped-tar file) also available at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

Collective excitations of Bose-Einstein condensed gases at finite temperatures

We have applied the Popov version of the Hartree-Fock-Bogoliubov (HFB) approximation to calculate the finite-temperature excitation spectrum of a Bose-Einstein condensate (BEC) of $^{87}$Rb atoms. For lower values of the temperature, we find excellent agreement with recently-published experimental data for the JILA TOP trap. In contrast to recent comparison of the results of HFB--Popov theory with experimental condensate fractions and specific heats, there is disagreement of the theoretical and recent experimental results near the BEC phase transition temperature.Comment: 4 pages, Latex, with 4 figures. More info at http://amo.phy.gasou.edu/bec.htm

Stability analysis of the D-dimensional nonlinear Schroedinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schroedinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D is greater or equal 2. In case D=2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse.Comment: 6 pages, 7 figure

Anterior communicating artery complex aneurysms: anatomic characteristics as predictors of surgical outcome in 300 cases

OBJECTIVE Anterior communicating artery (ACoA) complex aneurysms are challenging to treat microsurgically. The authors report their experience with microsurgical treatment of ACoA aneurysms and examine the anatomic characteristics of these aneurysms as predictors of outcome. METHODS The authors queried their institution’s aneurysm database for records of consecutive patients treated for ACoA aneurysms via microsurgical clip ligation. Data included patient demographics and clinical/radiographic presentation characteristics as well as operative techniques. Glasgow outcome scores (GOS) at hospital discharge and 6-month as well as 1-year follow-up were analyzed. RESULTS Of 319 ACoA aneurysms that underwent treatment, 259 were ruptured and 60 were unruptured. Average GOS at 1-year follow-up for all patients was 4.6. Average GOS for patients with ruptured aneurysms correlated with Hunt and Hess grade at presentation, presence of frontal hemorrhages, and need for multiple clips during surgery. Notably, 142 (44.5%) of aneurysms originated mainly from the ACoA artery; 12 (3.8%) primarily from the A1 branch; 3 (0.9%) from the A2 branch; and 162 (50.8%) from the A1/A2 junction. Aneurysm projection was superior in 118 (37%), inferior in 106 (33.2%), anterior in 88 (27.6%), and posterior in 7 (2.2%). Patients with aneurysms originating from the A1 segment had worse outcomes. Posteriorly-projecting aneurysms were more likely to be unruptured and larger than other aneurysm configurations. CONCLUSIONS The aneurysm’s exact location in relation to the adjacent neurovascular structures is potentially predictive of outcomes in the microsurgical treatment of ACoA aneurysms

Stabilizing an Attractive Bose-Einstein Condensate by Driving a Surface Collective Mode

Bose-Einstein condensates of $^7$Li have been limited in number due to attractive interatomic interactions. Beyond this number, the condensate undergoes collective collapse. We study theoretically the effect of driving low-lying collective modes of the condensate by a weak asymmetric sinusoidally time-dependent field. We find that driving the radial breathing mode further destabilizes the condensate, while excitation of the quadrupolar surface mode causes the condensate to become more stable by imparting quasi-angular momentum to it. We show that a significantly larger number of atoms may occupy the condensate, which can then be sustained almost indefinitely. All effects are predicted to be clearly visible in experiments and efforts are under way for their experimental realization.Comment: 4 ReVTeX pages + 2 postscript figure

Condensate fraction and critical temperature of a trapped interacting Bose gas

By using a mean field approach, based on the Popov approximation, we calculate the temperature dependence of the condensate fraction of an interacting Bose gas confined in an anisotropic harmonic trap. For systems interacting with repulsive forces we find a significant decrease of the condensate fraction and of the critical temperature with respect to the predictions of the non-interacting model. These effects go in the opposite direction compared to the case of a homogeneous gas. An analytic result for the shift of the critical temperature holding to first order in the scattering length is also derived.Comment: 8 pages, REVTEX, 2 figures, also available at http://anubis.science.unitn.it/~oss/bec/BEC.htm