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

Cross-lagged associations between depressive symptoms and response style in adolescents

Depressive disorders are highly prevalent during adolescence and they are a major concern for individuals and society. The Response Style Theory and the Scar Theory both suggest a relationship between response styles and depressive symptoms, but the theories differ in the order of the development of depressive symptoms. Longitudinal reciprocal prospective relationships between depressive symptoms and response styles were examined in a community sample of 1343 adolescents. Additionally, response style was constructed with the traditional approach, which involves examining three response styles separately without considering the possible relations between them, and with the ratio approach, which accounts for all three response styles simultaneously. No reciprocal relationships between depressive symptoms and response style were found over time. Only longitudinal relationships between response style and depressive symptoms were significant. This study found that only depressive symptoms predicted response style, whereas the response style did not emerge as an important underlying mechanism responsible for developing and maintaining depressive symptoms in adolescents. These findings imply that prevention and intervention programs for adolescents with low depressive symptoms should not focus on adaptive and maladaptive response style strategies to decrease depressive symptoms, but should focus more on behavioral interventions

Vortex lattice of a Bose-Einstein Condensate in a rotating anisotropic trap

We study the vortex lattices in a Bose-Einstein Condensate in a rotating anisotropic harmonic trap. We first investigate the single particle wavefunctions obtained by the exact solution of the problem and give simple expressions for these wavefunctions in the small anisotropy limit. Depending on the strength of the interactions, a few or a large number of vortices can be formed. In the limit of many vortices, we calculate the density profile of the cloud and show that the vortex lattice stays triangular. We also find that the vortex lattice planes align themselves with the weak axis of the external potential. For a small number of vortices, we numerically solve the Gross-Pitaevskii equation and find vortex configurations that are very different from the vortex configurations in an axisymmetric rotating trap.Comment: 15 pages,4 figure

Народное образование крымских татар в конце XIX - начале XX вв.: история и опыт в свете модернизации высшего образования Украины

Процесс модернизации высшего образования Украины проходит параллельно с процессом интеграции крымскотатарского населения в гражданское общество Украины.Процес модернізації вищого утворення України проходить паралельно з процесом інтеграції кримськотатарського населення в цивільне суспільство України

Anisotropic transport in the two-dimensional electron gas in the presence of spin-orbit coupling

In a two-dimensional electron gas as realized by a semiconductor quantum well, the presence of spin-orbit coupling of both the Rashba and Dresselhaus type leads to anisotropic dispersion relations and Fermi contours. We study the effect of this anisotropy on the electrical conductivity in the presence of fixed impurity scatterers. The conductivity also shows in general an anisotropy which can be tuned by varying the Rashba coefficient. This effect provides a method of detecting and investigating spin-orbit coupling by measuring spin-unpolarized electrical currents in the diffusive regime. Our approach is based on an exact solution of the two-dimensional Boltzmann equation and provides also a natural framework for investigating other transport effects including the anomalous Hall effect.Comment: 10 pages, 1 figure included. Discussion of experimental impact enlarged; error in calculation of conductivity contribution corrected (cf. Eq. (A14)), no changes in qualitative results and physical consequence

Macroscopic dynamics of a Bose-Einstein condensate containing a vortex lattice

Starting from the equations of rotational hydrodynamics we study the macroscopic behaviour of a trapped Bose-Einstein condensate containing a large number of vortices. The stationary configurations of the system, the frequencies of the collective excitations and the expansion of the condensate are investigated as a function of the angular velocity of the vortex lattice. The time evolution of the condensate and of the lattice geometry induced by a sudden deformation of the trap is also discussed and compared with the recent experimental results of P. Engels et al., Phys. Rev. Lett. 89, 100403 (2002).Comment: 4 pages, 4 figure

Nanofabrication by magnetic focusing of supersonic beams

We present a new method for nanoscale atom lithography. We propose the use of a supersonic atomic beam, which provides an extremely high-brightness and cold source of fast atoms. The atoms are to be focused onto a substrate using a thin magnetic film, into which apertures with widths on the order of 100 nm have been etched. Focused spot sizes near or below 10 nm, with focal lengths on the order of 10 microns, are predicted. This scheme is applicable both to precision patterning of surfaces with metastable atomic beams and to direct deposition of material.Comment: 4 pages, 3 figure

Deconfining Phase Transition as a Matrix Model of Renormalized Polyakov Loops

We discuss how to extract renormalized from bare Polyakov loops in SU(N) lattice gauge theories at nonzero temperature in four spacetime dimensions. Single loops in an irreducible representation are multiplicatively renormalized without mixing, through a renormalization constant which depends upon both representation and temperature. The values of renormalized loops in the four lowest representations of SU(3) were measured numerically on small, coarse lattices. We find that in magnitude, condensates for the sextet and octet loops are approximately the square of the triplet loop. This agrees with a large $N$ expansion, where factorization implies that the expectation values of loops in adjoint and higher representations are just powers of fundamental and anti-fundamental loops. For three colors, numerically the corrections to the large $N$ relations are greatest for the sextet loop, $\leq 25$; these represent corrections of $\sim 1/N$ for N=3. The values of the renormalized triplet loop can be described by an SU(3) matrix model, with an effective action dominated by the triplet loop. In several ways, the deconfining phase transition for N=3 appears to be like that in the $N=\infty$ matrix model of Gross and Witten.Comment: 24 pages, 7 figures; v2, 27 pages, 12 figures, extended discussion for clarity, results unchange

Spin-current modulation and square-wave transmission through periodically stubbed electron waveguides

Ballistic spin transport through waveguides, with symmetric or asymmetric double stubs attached to them periodically, is studied systematically in the presence of a weak spin-orbit coupling that makes the electrons precess. By an appropriate choice of the waveguide length and of the stub parameters injected spin-polarized electrons can be blocked completely and the transmission shows a periodic and nearly square-type behavior, with values 1 and 0, with wide gaps when only one mode is allowed to propagate in the waveguide. A similar behavior is possible for a certain range of the stub parameters even when two-modes can propagate in the waveguide and the conductance is doubled. Such a structure is a good candidate for establishing a realistic spin transistor. A further modulation of the spin current can be achieved by inserting defects in a finite-number stub superlattice. Finite-temperature effects on the spin conductance are also considered.Comment: 19 pages, 8 figure

Vortices and dynamics in trapped Bose-Einstein condensates

I review the basic physics of ultracold dilute trapped atomic gases, with emphasis on Bose-Einstein condensation and quantized vortices. The hydrodynamic form of the Gross-Pitaevskii equation (a nonlinear Schr{\"o}dinger equation) illuminates the role of the density and the quantum-mechanical phase. One unique feature of these experimental systems is the opportunity to study the dynamics of vortices in real time, in contrast to typical experiments on superfluid $^4$He. I discuss three specific examples (precession of single vortices, motion of vortex dipoles, and Tkachenko oscillations of a vortex array). Other unusual features include the study of quantum turbulence and the behavior for rapid rotation, when the vortices form dense regular arrays. Ultimately, the system is predicted to make a quantum phase transition to various highly correlated many-body states (analogous to bosonic quantum Hall states) that are not superfluid and do not have condensate wave functions. At present, this transition remains elusive. Conceivably, laser-induced synthetic vector potentials can serve to reach this intriguing phase transition.Comment: Accepted for publication in Journal of Low Temperature Physics, conference proceedings: Symposia on Superfluids under Rotation (Lammi, Finland, April 2010