Bose-Einstein Condensates with Large Number of Vortices

We show that as the number of vortices in a three dimensional Bose-Einstein Condensate increases, the system reaches a "quantum Hall" regime where the density profile is a Gaussian in the xy-plane and an inverted parabolic profile along z. The angular momentum of the system increases as the vortex lattice shrinks. However, Coriolis force prevents the unit cell of the vortex lattice from shrinking beyond a minimum size. Although the recent MIT experiment is not exactly in the quantum Hall regime, it is close enough for the present results to be used as a guide. The quantum Hall regime can be easily reached by moderate changes of the current experimental parameters.Comment: 4 pages, no figure

Running anti-de Sitter radius from QCD-like strings

We consider renormalization effects for a bosonic QCD-like string, whose partons have $1/p^{2}$ propagators instead of Gaussian. Classically this model resembles (the bosonic part of) the projective light-cone (zero-radius) limit of a string on an AdS${}_5$ background, where Schwinger parameters give rise to the fifth dimension. Quantum effects generate dynamics for this dimension, producing an AdS${}_5$ background with a running radius. The projective light-cone is the high-energy limit: Holography is enforced dynamically.Comment: 12 page

A node-to-node scheme for three-dimensional contact problems using the scaled boundary finite element method

A node-to-node (NTN) scheme for modeling three-dimensional contact problems within a scaled boundary finite element method (SBFEM) framework is proposed. Polyhedral elements with an arbitrary number of faces and nodes are constructed using the SBFEM. Only the boundary of the polyhedral element is discretized to accommodate a higher degree of flexibility in mesh transitioning. Nonmatching meshes can be simply converted into matching ones by appropriate node insertions, thereby allowing the use of a favorable NTN contact scheme. The general three-dimensional frictional contact is explicitly formulated as a mixed complementarity problem (MCP). The inherent nonlinearity in the three-dimensional friction condition is treated accurately without requiring piecewise linearization. Contact constraints for non-penetration and stick-slide are enforced directly in a complementarity format. Numerical examples with 1st and 2nd order elements demonstrate the accuracy and robustness of the proposed scheme

Two-component Bose-Einstein Condensates with Large Number of Vortices

We consider the condensate wavefunction of a rapidly rotating two-component Bose gas with an equal number of particles in each component. If the interactions between like and unlike species are very similar (as occurs for two hyperfine states of $^{87}$Rb or $^{23}$Na) we find that the two components contain identical rectangular vortex lattices, where the unit cell has an aspect ratio of $\sqrt{3}$, and one lattice is displaced to the center of the unit cell of the other. Our results are based on an exact evaluation of the vortex lattice energy in the large angular momentum (or quantum Hall) regime.Comment: 4 pages, 2 figures, RevTe

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

Spinor Bose Condensates in Optical Traps

In an optical trap, the ground state of spin-1 Bosons such as $^{23}$Na, $^{39}$K, and $^{87}$Rb can be either a ferromagnetic or a "polar" state, depending on the scattering lengths in different angular momentum channel. The collective modes of these states have very different spin character and spatial distributions. While ordinary vortices are stable in the polar state, only those with unit circulation are stable in the ferromagnetic state. The ferromagnetic state also has coreless (or Skyrmion) vortices like those of superfluid $^{3}$He-A. Current estimates of scattering lengths suggest that the ground states of $^{23}$Na and $^{87}$Rb condensate are a polar state and a ferromagnetic state respectively.Comment: 11 pages, no figures. email : [email protected]

Multiple-Scattering Suppression by Cross Correlation

We describe a new method for characterizing particles in turbid media by cross correlating the scattered intensity fluctuations at two nearby points in the far field. The cross-correlation function selectively emphasizes single scattering over multiple scattering. The usual dynamic light-scattering capability of inferring particle size from decay rate is thus extended to samples that are so turbid as to be visually opaque. The method relies on single-scattering speckle being physically larger than multiple-scattering speckle. With a suitable optical geometry to select nearby points in the far field or equivalently slightly different scattering wave vectors (of the same magnitude), the multiple-scattering contribution to the cross-correlation function may be reduced and in some cases rendered insignificant. Experimental results demonstrating the feasibility of this approach are presented. (C) 1997 Optical Society of America

Multiple-Scattering Suppression by Cross Correlation

We describe a new method for characterizing particles in turbid media by cross correlating the scattered intensity fluctuations at two nearby points in the far field. The cross-correlation function selectively emphasizes single scattering over multiple scattering. The usual dynamic light-scattering capability of inferring particle size from decay rate is thus extended to samples that are so turbid as to be visually opaque. The method relies on single-scattering speckle being physically larger than multiple-scattering speckle. With a suitable optical geometry to select nearby points in the far field or equivalently slightly different scattering wave vectors (of the same magnitude), the multiple-scattering contribution to the cross-correlation function may be reduced and in some cases rendered insignificant. Experimental results demonstrating the feasibility of this approach are presented. (C) 1997 Optical Society of America