We demonstrate the existence of phase fluctuations in elongated Bose-Einstein Condensates (BECs) and study the dependence of those fluctuations on the system parameters. A strong dependence on temperature , atom number, and trapping geometry is observed. Phase fluctuations directly affect the coherence properties of BECs. In particular, we observe instances where the phase coherence length is s...

We demonstrate that a Bose-Einstein condensate in an optical lattice forms a reconfigurable matter-wave structure with a band-gap spectrum, which resembles a nonlinear photonic crystal for light waves. We study in detail the case of a two-dimensional square optical lattice and show that this atomic band-gap structure allows nonlinear localization of atomic Bloch waves in the form of two-dimensi...

Brill waves are the simplest (non-trivial) solutions to the vacuum constraints of general relativity. They are also rich enough in structure to allow us believe that they capture, at least in part, the generic properties of solutions of the Einstein equations. As such, they deserve the closest attention. This article illustrates this point by showing how Brill waves can be used to investigate t...

A major difficulty with conventional formulations of euclidean quantum gravity is the fact that the Einstein action I, can become arbitrarily negative [l]. This means that the path integral of exp( -In) does not converge. The problem persists for lattice formulations of gravity [2] and provides an obstacle to progress for calculations of anything other than the weak field limit [3]. A possible ...

Using the covariant approach and conformal transformations, we present a gauge-invariant formalism for cosmological perturbations in generalized Einstein theories (GETs), including the Brans-Dicke theory, theories with a non-minimally coupled scalar field and certain curvature-squared theories. We find an enhancement in the growth rate of density perturbations in the Brans-Dicke theory, and dis...

We analyze spatiotemporal structures in the Gross-Pitaevskii equation to study the dynamics of quasi-one-dimensional Bose-Einstein condensates (BECs) with mean-field interactions. A coherent structure ansatz yields a parametrically forced nonlinear oscillator, to which we apply Lindstedt's method and multiple-scale perturbation theory to determine the dependence of the intensity of periodic orb...

in this paper, the matsumoto metric with special ricci tensor has been investigated. it is proved that, if  is ofpositive (negative) sectional curvature and f is of  -parallel ricci curvature with constant killing 1-form ,then (m,f) is a riemannian einstein space. in fact, we generalize the riemannian result established by akbar-zadeh.

We investigate rogue-wave solutions in a three-component coupled nonlinear Schrödinger equation. With certain requirements on the backgrounds of components, we construct a multi-rogue-wave solution that exhibits a structure like a four-petaled flower in temporal-spatial distribution, in contrast to the eye-shaped structure in one-component or two-component systems. The results could be of inter...

We consider the vortex structure of a rapidly rotating trapped atomic Bose-Einstein condensate in the presence of a corotating periodic optical lattice potential. We observe a rich variety of structural phases which reflect the interplay of the vortex-vortex and vortex-lattice interactions. The lattice structure is very sensitive to the ratio of vortices to pinning sites and we observe structur...

Let M be a compact complex manifold of complex dimension two with a smooth Kahler metric and D a smooth divisor on M. If E is a rank 2 holomorphic vector bundle on M with a stable parabolic structure along D, we prove that there exists a Hermitian-Einstein metric on E' = E|M\D compatible with the parabolic structure, and whose curvature is square integrable. MIRAMARE TRIESTE January 2000