Construction of exact solutions by spatial traslations in inhomogeneous Nonlinear Schrodinger equations. Applications to Bose-Einstein condensation

In this paper we study a general nonlinear Schr\"odinger equation with a time dependent harmonic potential. Despite the lack of traslational invariance we find a symmetry trasformation which, up from any solution, produces infinitely many others which are centered on classical trajectories. The results presented here imply that, not only the center of mass of the wave-packet satisfies the Ehrenfest theorem and is decoupled from the dynamics of the wave-packet, but also the shape of the solution is independent of the behaviour of the center of the wave. Our findings have implications on the dynamics of Bose-Einstein condensates in magnetic trapsComment: Submitted to Phys. Re

Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps

We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. Using simple arguments, we derive expressions for the velocity field of the quantum fluid for condensates with or without vortices. While the condensed gas describes open spiraling trajectories, on the frame of reference of the rotating trap the motion of the fluid is against the trap rotation. We also find explicit formulae for the angular momentum and a linear and Thomas-Fermi solutions for the state without vortices. In these two limits we also find an analytic relation between the shape of the cloud and the rotation speed. The predictions are supported by numerical simulations of the mean field Gross-Pitaevskii model.Comment: 4 RevTeX pages, 2 EPS figures; typos fixed, reference adde

Anti-factor Xa antibodies in patients with antiphospholipid syndrome and their effects upon coagulation assays

- Introduction: The aim of this study was to examine the prevalence and functional effects of antibodies directed against Factor (F)Xa and other serine proteases (SP) in patients with antiphospholipid syndrome (APS). - Methods: Serum from patients with APS (n = 59), systemic lupus erythematosus (SLE; n = 106), other autoimmune rheumatic disease (ARD; n = 63) and 40 healthy controls (HC) were tested for IgG activity against thrombin (Thr), FXa, FVIIa, phosphatidylserine (PS)/FXa and antithrombin (AT)-III by enzyme-linked immunosorbent assay (ELISA). Anti-FXa positive IgG were purified to measure their avidity by chaotropic ELISA and functional effects upon clotting time (FXa-ACT) and FXa enzymatic activity (± AT-III). - Results: Anti-FXa IgG were found in patients with SLE (49.1%) and APS (33.9%) (P <0.05) but not in ARD controls and HC. In contrast, anti-Thr and anti-PS/FXa IgG were identified in other ARD and anti-FVIIa IgG were low in all groups. The avidity of APS-IgG to FXa was significantly higher than SLE-IgG (P <0.05). Greatest prolongation of FXa-ACT was observed with APS-IgG and greatest inhibitory effect upon FXa enzymatic activity was found with APS-IgG followed by SLE-IgG compared to HC-IgG. ATIII inhibition of FXa was significantly reduced by APS-IgG compared with HC and SLE (P <0.05) and did not correlate with binding to AT-III. - Conclusion: APS anti-FXa IgG have higher avidity to FXa and greater effects upon the enzymatic and coagulant activity of FXa compared with SLE anti-FXa IgG. Further studies of anti-FXa antibodies in APS, SLE and other non-autoimmune thrombotic disease cohorts are now required to evaluate whether targeting FXa with selective inhibitors in patients bearing anti-FXa antibodies may be an effective treatment strategy

Small-amplitude normal modes of a vortex in a trapped Bose-Einstein condensate

We consider a cylindrically symmetric trap containing a small Bose-Einstein condensate with a singly quantized vortex on the axis of symmetry. A time-dependent variational Lagrangian analysis yields the small-amplitude dynamics of the vortex and the condensate, directly determining the equations of motion of the coupled normal modes. As found previously from the Bogoliubov equations, there are two rigid dipole modes and one anomalous mode with a negative frequency when seen in the laboratory frame.Comment: 4 pages, no figures, Revte

Solutions of Gross-Pitaevskii equations beyond the hydrodynamic approximation: Application to the vortex problem

We develop the multiscale technique to describe excitations of a Bose-Einstein condensate (BEC) whose characteristic scales are comparable with the healing length, thus going beyond the conventional hydrodynamical approximation. As an application of the theory we derive approximate explicit vortex and other solutions. The dynamical stability of the vortex is discussed on the basis of the mathematical framework developed here, the result being that its stability is granted at least up to times of the order of seconds, which is the condensate lifetime. Our analytical results are confirmed by the numerical simulations.Comment: To appear in Phys. Rev.

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure

Stability and collapse of localized solutions of the controlled three-dimensional Gross-Pitaevskii equation

On the basis of recent investigations, a newly developed analytical procedure is used for constructing a wide class of localized solutions of the controlled three-dimensional (3D) Gross-Pitaevskii equation (GPE) that governs the dynamics of Bose-Einstein condensates (BECs). The controlled 3D GPE is decomposed into a two-dimensional (2D) linear Schr\"{o}dinger equation and a one-dimensional (1D) nonlinear Schr\"{o}dinger equation, constrained by a variational condition for the controlling potential. Then, the above class of localized solutions are constructed as the product of the solutions of the transverse and longitudinal equations. On the basis of these exact 3D analytical solutions, a stability analysis is carried out, focusing our attention on the physical conditions for having collapsing or non-collapsing solutions.Comment: 21 pages, 14 figure

Evaluation of turbulent dissipation rate retrievals from Doppler Cloud Radar

Turbulent dissipation rate retrievals from cloud radar Doppler velocity measurements are evaluated using independent, in situ observations in Arctic stratocumulus clouds. In situ validation data sets of dissipation rate are derived using sonic anemometer measurements from a tethered balloon and high frequency pressure variation observations from a research aircraft, both flown in proximity to stationary, ground-based radars. Modest biases are found among the data sets in particularly low- or high-turbulence regimes, but in general the radar-retrieved values correspond well with the in situ measurements. Root mean square differences are typically a factor of 4-6 relative to any given magnitude of dissipation rate. These differences are no larger than those found when comparing dissipation rates computed from tetheredballoon and meteorological tower-mounted sonic anemometer measurements made at spatial distances of a few hundred meters. Temporal lag analyses suggest that approximately half of the observed differences are due to spatial sampling considerations, such that the anticipated radar-based retrieval uncertainty is on the order of a factor of 2-3. Moreover, radar retrievals are clearly able to capture the vertical dissipation rate structure observed by the in situ sensors, while offering substantially more information on the time variability of turbulence profiles. Together these evaluations indicate that radar-based retrievals can, at a minimum, be used to determine the vertical structure of turbulence in Arctic stratocumulus clouds

Solitary waves for linearly coupled nonlinear Schrodinger equations with inhomogeneous coefficients

Motivated by the study of matter waves in Bose-Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrodinger equations with inhomogeneous parameters, including a linear coupling. For that system we prove the existence of two different kinds of homoclinic solutions to the origin describing solitary waves of physical relevance. We use a Krasnoselskii fixed point theorem together with a suitable compactness criterion.Comment: 16 page

Results of the material screening program of the NEXT experiment

[EN] The Neutrino Experiment with a Xenon TPC (NEXT), intended to investigate neutrinoless double beta decay, requires extremely low background levels. An extensive material screening and selection process to assess the radioactivity of components is underway combining several techniques, including germanium &#947;-ray spectrometry performed at the Canfranc Underground Laboratory; recent results of this material screening program are presented here.Dafni, T.; Álvarez-Puerta, V.; Bandac, I.; Bettini, A.; Borges, FIGM.; Camargo, M.; Carcel, S.... (2016). Results of the material screening program of the NEXT experiment. Nuclear and Particle Physics Proceedings. 273-275:2666-2668. https://doi.org/10.1016/j.nuclphysbps.2015.10.024S26662668273-27