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

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.

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

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

Tumor testicular de saco vitelino con metástasis a pleura: primer caso reportado en la literatura

ResumenEl cáncer testicular es el tumor urológico maligno más común en hombres jóvenes. Más del 90% corresponden a tumores de células germinales. El objetivo del estudio es el reporte del primer caso de cáncer testicular de tumores de células germinales con metástasis a pleura.Paciente masculino de 21 años, inicia su padecimiento con dolor en hemitórax derecho; la radiografía de tórax presenta una radioopacidad en lóbulo medio de pulmón derecho y la tomografía de tórax detecta una masa intratorácica y extrapulmonar. La biopsia torácica guiada por ultrasonido muestra una masa sólida adosada a la pared torácica, con efecto de desplazamiento sobre la pleura, conocido como «efecto en cola de cometa». La biopsia fue positiva para lesión neoplásica maligna poco diferenciada de la pleura. A la exploración encontramos testículo derecho con tumoración en polo inferior el cual se corrobora por ultrasonido. Los marcadores tumorales solo con elevación de alfa-fetoproteína 295.87ng/dL y deshidrogenasa láctica en 2,380UI/L. En la tomografía de abdomen se identificó actividad ganglionar interaortocava. Realizamos orquiectomía radical derecha. Reporte patológico: tumor testicular de saco vitelino, pT1N2M1S2.En este caso se pudo comprobar que las metástasis fueron a nivel pleural, que lo ubica como una forma de diseminación excepcional.AbstractTesticular cancer is the most common malignant urologic tumor in young men. More than 90% are germ cell tumors. The aim of this study was to report the first case of germ cell tumor testicular cancer with metastasis to the pleura.A 21-year-old man had disease onset with pain in the right hemithorax. The chest x-ray showed radio-opacity in the middle lobe of the right lung. A chest tomography scan detected an intrathoracic and extrapulmonary mass. Ultrasound-guided thoracic biopsy revealed a solid mass attached to the thoracic wall, displaced over the pleura, known as the “comet tail effect”. The biopsy was positive for a poorly differentiated malignant neoplastic lesion of the pleura. Upon physical examination we encountered a right testis with a tumor at the lower pole; this was corroborated through ultrasound. In relation to tumor markers, only alpha-fetoprotein was elevated at 295.87ng/dl and lactate dehydrogenase at 2,380 IU/l. An abdominal tomography scan identified interaortocaval lymph node activity. We performed a right radical orchiectomy and the pathology report was testicular yolk sac tumor, pT1N2M1S2.In our patient, metastasis at the level of the pleura was confirmed, making this a case with an exceptional form of spread

Excitations of a Bose-condensed gas in anisotropic traps

We investigate the zero-temperature collective excitations of a Bose-condensed atomic gas in anisotropic parabolic traps. The condensate density is determined by solving the Gross-Pitaevskii (GP) equation using a spherical harmonic expansion. The GP eigenfunctions are then used to solve the Bogoliubov equations to obtain the collective excitation frequencies and mode densities. The frequencies of the various modes, classified by their parity and the axial angular momentum quantum number, m, are mapped out as a function of the axial anisotropy. Specific emphasis is placed upon the evolution of these modes from the modes in the limit of an isotropic trap.Comment: 7 pages Revtex, 9 Postscript figure

Resistance to DNA Damaging agents produced invasive phenotype of rat glioma cells-characterization of a new in vivo model

Chemoresistance and invasion properties are severe limitations to efficient glioma therapy. Therefore, development of glioma in vivo models that more accurately resemble the situation observed in patients emerges. Previously, we established RC6 rat glioma cell line resistant to DNA damaging agents including antiglioma approved therapies such as 3-bis(2-chloroethyl)-1-nitrosourea (BCNU) and temozolomide (TMZ). Herein, we evaluated the invasiveness of RC6 cells in vitro and in a new orthotopic animal model. For comparison, we used C6 cells from which RC6 cells originated. Differences in cell growth properties were assessed by real-time cell analyzer. Cells’ invasive potential in vitro was studied in fluorescently labeled gelatin and by formation of multicellular spheroids in hydrogel. For animal studies, fluorescently labeled cells were inoculated into adult male Wistar rat brains. Consecutive coronal and sagittal brain sections were analyzed 10 and 25 days post-inoculation, while rats’ behavior was recorded during three days in the open field test starting from 25th day post-inoculation. We demonstrated that development of chemoresistance induced invasive phenotype of RC6 cells with significant behavioral impediments implying usefulness of orthotopic RC6 glioma allograft in preclinical studies for the examination of new approaches to counteract both chemoresistance and invasion of glioma cells

Stability of Attractive Bose-Einstein Condensates in a Periodic Potential

Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schr\"odinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.Comment: 12 pages, 18 figure

Oscillations of a rapidly rotating annular Bose-Einstein condensate

A time-dependent variational Lagrangian analysis based on the Gross-Pitaevskii energy functional serves to study the dynamics of a metastable giant vortex in a rapidly rotating Bose-Einstein condensate. The resulting oscillation frequencies of the core radius reproduce the trends seen in recent experiments [Engels et al., Phys. Rev. Lett. 90, 170405 (2003)], but the theoretical values are smaller by a factor approximately 0.6-0.8.Comment: 7 pages, revtex

Hydrodynamic Approach to Vortex Lifetime in Trapped Bose Condensates

We study a vortex in a two-dimensional, harmonically trapped Bose-Einstein condensate at zero temperature. Through a variational calculation using a trial condensate wave function and a nonlinear Schroedinger Lagrangian, we obtain the effective potential experienced by a vortex at an arbitrary position in the condensate, and find that an off-center vortex will move in a circular trajectory around the trap center. We find the frequency of this precession to be smaller than the elementary excitation frequencies in the cloud. We also study the radiation of sound from a moving vortex in an infinite, uniform system, and discuss the validity of this as an approximation for the trapped case. Furthermore, we estimate the lifetime of a vortex due to imperfections in the trapping potential.Comment: 10 pages, 1 eps figure, submitted to PRA, adjustments in response to referee, one refernce adde