We have measured the relative phase of two Bose-Einstein condensates (BEC) using a time-domain separated-oscillatory-field condensate interferometer. A single two-photon coupling pulse prepares the double condensate system with a well-defined relative phase; at a later time, a second pulse reads out the phase difference accumulated between the two condensates. We find that the accumulated phase...

We employ KAM theory to rigorously investigate the transition between quasiperiodic and chaotic dynamics in cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and superlattices. Toward this end, we apply ∗Corresponding author

Purely time dependent solutions in four-dimensional Einstein-CartanKalb-Ramond (ECKR) theory of gravity are shown not to be possible leading to a trivial vanishing of all Kalb-Ramond fields. This result seems to contradict previously results obtained by SenGupta et al. (Class. and Quantum Gravity 19(2002)677) where de Sitter spacetime solution is found as an example of opticaly active spacetime...

We classify solvable Lie groups with a free nilradical admitting an Einstein left-invariant metric. Any such group is essentially determined by the nilradical of its Lie algebra, which is then called an Einstein nilradical. We show that among the free Lie algebras, there are very few Einstein nilradicals. Except for the one-step (abelian) and the two-step ones, there are only six (here f(m, p) ...

It is of fundamental interest to study the geometric and analytic properties of compact Einstein manifolds and their moduli. In dimension 2 these problems are well understood. A 2-dimensional Einstein manifold, (M, g), has constant curvature, which after normalization, can be taken to be −1, 0 or 1. Thus, (M, g) is the quotient of a space form and the metric, g, is completely determined by the ...

We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski–Demianski metrics one obtains a family of local toric Kähler–Einstein metrics. These can be used to construct local Sasaki–Einstein metrics in five dimensions, which are generalisations of the Y p,q metrics. In fact, we find that the local metrics are diffeomorphic to those recently found by Cvetic, Lu, Page...

A Riemannian metric is said to be Einstein if the Ricci curvature is a constant multiple of the metric. Given a manifold M , one can ask whether M carries an Einstein metric, and if so, how many. This fundamental question in Riemannian geometry is for the most part unsolved (cf. [Bes]). As a global PDE or a variational problem, the question is intractible. It becomes more manageable in the homo...

We show that by taking a certain scaling limit of a Euclideanised form of the Plebanski–Demianski metrics one obtains a family of local toric Kähler–Einstein metrics. These can be used to construct local Sasaki–Einstein metrics in five dimensions which are generalisations of the Y p,q manifolds. In fact, we find that these metrics are diffeomorphic to those recently found by Cvetic, Lu, Page an...

Burris, Stanley. ‘‘George Boole.’’ In The Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. 2010. Available from http://plato.stanford.edu/archives/sum2010/entries/boole/ Krantz, Steven G. Discrete Mathematics Demystified. New York: McGraw-Hill, 2009. Nahin, Paul J. The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age. Princeton, NJ: Princ...

A Riemannian Einstein solvmanifold (possibly, any noncompact homogeneous Einstein space) is almost completely determined by the nilradical of its Lie algebra. A nilpotent Lie algebra, which can serve as the nilradical of an Einstein metric solvable Lie algebra, is called an Einstein nilradical. Despite a substantial progress towards the understanding of Einstein nilradicals, there is still a la...