Mass in K\"ahler Geometry

We prove a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) K\"ahler manifold, assuming only the sort of weak fall-off conditions required for the mass to actually be well-defined. For ALE scalar-flat K\"ahler manifolds, the mass turns out to be a topological invariant, depending only on the underlying smooth manifold, the first Chern class of the complex structure, and the K\"ahler class of the metric. When the metric is actually AE (asymptotically Euclidean), our formula not only implies a positive mass theorem for K\"ahler metrics, but also yields a Penrose-type inequality for the mass.Comment: 53 pages, minor corrections and improvements, final versio

The evolution of free wave packets

We discuss four general features of force-free evolution: (1) The spatial spread of any packet changes with time in a very simple way. (2) Over sufficiently short periods of time (whose duration is related to the spread in momentum of the packet) the probability distribution moves but there is little change in shape. (3) After a sufficiently long period (related to the initial spatial spread) the packet settles into a simple form simply related to the momentum distribution in the packet. In this asymptotic regime, the shape of the probability distribution no longer changes except for its scale, which increases linearly with the time. (4) There is an infinite denumerable set of simple wave packets (the Hermite-Gauss packets) that do not change shape as they evolve.Comment: 6 pages, 4 figures, didactic pape

Reversible Destruction of Dynamical Localization

Dynamical localization is a localization phenomenon taking place, for example, in the quantum periodically-driven kicked rotor. It is due to subtle quantum destructive interferences and is thus of intrinsic quantum origin. It has been shown that deviation from strict periodicity in the driving rapidly destroys dynamical localization. We report experimental results showing that this destruction is partially reversible when the deterministic perturbation that destroyed it is slowly reversed. We also provide an explanation for the partial character of the reversibility.Comment: 4 pages, 2 eps figures (color

Quantum limits in image processing

We determine the bound to the maximum achievable sensitivity in the estimation of a scalar parameter from the information contained in an optical image in the presence of quantum noise. This limit, based on the Cramer-Rao bound, is valid for any image processing protocol. It is calculated both in the case of a shot noise limited image and of a non-classical illumination. We also give practical experimental implementations allowing us to reach this absolute limit.Comment: 4 pages, two figure

Hétérogéneités du manteau et origine des basaltes des Marquises (Polynésie)

Les auteurs discutent les connaissances bibliographiques concernant les hétérogénéités isotopiques du manteau et les processus les engendrant. Par l'étude conjointe des isotopes et des traces ils abordent la genèse des basaltes des Marquises. Leurs caractéristiques géochimiques suggèrent un modèle d'interaction de magmas d'origine profonde avec le manteau supérieur appauvri. Puisqu'elles sont très différentes de celles des basaltes des îles Hawaii, les auteurs supposent que l'on peut proposer plusieurs modèles pour la genèse du volcanisme intraplaque océanique

A quantum study of multi-bit phase coding for optical storage

We propose a scheme which encodes information in both the longitudinal and spatial transverse phases of a continuous-wave optical beam. A split detector-based interferometric scheme is then introduced to optimally detect both encoded phase signals. In contrast to present-day optical storage devices, our phase coding scheme has an information storage capacity which scales with the power of the read-out optical beam. We analyse the maximum number of encoding possibilities at the shot noise limit. In addition, we show that using squeezed light, the shot noise limit can be overcome and the number of encoding possibilities increased. We discuss a possible application of our phase coding scheme for increasing the capacities of optical storage devices.Comment: 8 pages, 7 figures (Please email author for a PDF file if the manuscript does not turn out properly