The structure of a solvable Lie groups admitting an Einstein left-invariant metric is, in a sense, completely determined by the nilradical of its Lie algebra. We give an easy-to-check necessary and sufficient condition for a nilpotent algebra to be an Einstein nilradical whose Einstein derivation has simple eigenvalues. As an application, we classify filiform Einstein nilradicals (modulo known ...

Suppose M a compact manifold which admits an Einstein metric g which is Kähler with respect to some complex structure J . Is every other Einstein metric h on M also Kähler-Einstein? If the complex dimension of (M,J) is ≥ 3, the answer is generally no; for example, CP3 admits both the FubiniStudy metric, which is Kähler-Einstein, and a non-Kähler Einstein metric [2] obtained by appropriately squ...

A theorem of Følner asserts that for any set A ⊂ Z of positive upper density there is a Bohr neigbourhood B of 0 such that B \ (A − A) has zero density. We use this result to deduce some consequences about the structure of difference sets of sets of integers having a positive upper density.

We study the existence of projectable G-invariant Einstein metrics on the total space of G-equivariant fibrations M = G/L → G/K, for a compact connected semisimple Lie group G. We obtain necessary conditions for the existence of such Einstein metrics in terms of appropriate Casimir operators, which is a generalization of the result by Wang and Ziller about Einstein normal metrics. We describe b...

A number of recent surveys for gravitational lenses have found examples of double Einstein rings. Here, we investigate analytically the occurence of multiple Einstein rings. We prove, under very general assumptions, that at most one Einstein ring can arise from a mass distribution in a single plane lensing a single background source. Two or more Einstein rings can therefore only occur in multi-...

The subject of left-invariant Ricci soliton metrics on nilpotent Lie groups has enjoyed quite a bit of attention in the past several years. These metrics are intimately related to left-invariant Einstein metrics on non-unimodular solvable Lie groups. In fact, a classification of one is equivalent to a classification of the other. In this note, we focus our attention on nilpotent Lie groups and ...

Submitted for the MAR08 Meeting of The American Physical Society Interference between atomic Bardeen-Cooper-Schrieffer gases TUN WANG, Austrian Academy of Science, SUSANNE YELIN, Univ. of Connecticut — We study the interference between two atomic Bardeen-CooperSchrieffer (BCS) gases using noise correlations. Fringes as seen in the interference between two Bose-Einstein Condensates (BECs) do not...

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...