Eisenstein integrals and induction of relations

I give a survey of joint work with Henrik Schlichtkrull on the induction of certain relations among (partial) Eisenstein integrals for the minimal principal series of a reductive symmetric space. I explain the application of this principle of induction to the proofs of a Fourier inversion formula and a Paley-Wiener theorem. Finally, the relation with the Plancherel decomposition is discussed.Comment: Latex2e, 22 pp, Proc. Conf. `Analyse Harmonique Non Commutative (colloque en l'honneur de Jacques Carmona)' CIRM, Luminy, 20-24 Mai, 200

A Paley-Wiener theorem for reductive symmetric spaces

Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. The image under the Fourier transform of the space of K-finite compactly supported smooth functions on X is characterized.Comment: 31 pages, published versio

Paley-Wiener spaces for real reductive Lie groups

We show that Arthur's Paley-Wiener theorem for K-finite compactly supported smooth functions on a real reductive Lie group G of the Harish-Chandra class can be deduced from the Paley-Wiener theorem we established in the more general setting of a reductive symmetric space. In addition, we formulate an extension of Arthur's theorem to K-finite compactly supported generalized functions (distributions) on G and show that this result follows from the analogous result for reductive symmetric spaces as well.Comment: Latex2e, 28 pages, change of definition of space P^* on p. 17 + minor correction

The microlensing rate and distribution of free-floating planets towards the Galactic bulge

Ground-based optical microlensing surveys have provided tantalising, if inconclusive, evidence for a significant population of free-floating planets (FFPs). Both ground and space-based facilities are being used and developed which will be able to probe the distrubution of FFPs with much better sensitivity. It is vital also to develop a high-precision microlensing simulation framework to evaluate the completeness of such surveys. We present the first signal-to-noise limited calculations of the FFP microlensing rate using the Besancon Galactic model. The microlensing distribution towards the Galactic centre is simulated for wide-area ground-based optical surveys such as OGLE or MOA, a wide-area ground-based near-IR survey, and a targeted space-based near-IR survey which could be undertaken with Euclid or WFIRST. We present a calculation framework for the computation of the optical and near-infrared microlensing rate and optical depth for simulated stellar catalogues which are signal-to-noise limited, and take account of extinction, unresolved stellar background light and finite source size effects, which can be significant for FFPs. We find that the global ground-based I-band yield over a central 200 deg^2 region covering the Galactic centre ranges from 20 Earth-mass FFPs year^-1 up to 3,500 year^-1 for Jupiter FFPs in the limit of 100% detection efficiency, and almost an order of magnitude larger for a K-band survey. For ground-based surveys we find that the inclusion of finite source and the unresolved background reveals a mass-dependent variation in the spatial distribution of FFPs. For a space-based H-band covering 2 deg^2, the yield depends on the target field but maximizes close to the Galactic centre with around 76 Earth through to 1,700 Jupiter FFPs year^-1. For near-IR space-based surveys the spatial distribution of FFPs is found to be largely insensitive to the FFP mass scale.Comment: 14 pages, submitted to A&A and accepte

Explanation and observability of diffraction in time

Diffraction in time (DIT) is a fundamental phenomenon in quantum dynamics due to time-dependent obstacles and slits. It is formally analogous to diffraction of light, and is expected to play an increasing role to design coherent matter wave sources, as in the atom laser, to analyze time-of-flight information and emission from ultrafast pulsed excitations, and in applications of coherent matter waves in integrated atom-optical circuits. We demonstrate that DIT emerges robustly in quantum waves emitted by an exponentially decaying source and provide a simple explanation of the phenomenon, as an interference of two characteristic velocities. This allows for its controllability and optimization.Comment: 4 pages, 6 figure

Precision measurements in nuclear {\beta}-decay with LPCTrap

The experimental achievements and the current program with the LPCTrap device installed at the LIRAT beam line of the SPIRAL1-GANIL facility are presented. The device is dedicated to the study of the weak interaction at low energy by means of precise measurements of the {\beta}-{\nu} angular correlation parameter. Technical aspects as well as the main results are reviewed. The future program with new available beams is briefly discussed.Comment: Annalen der Physik (2013