12,248 research outputs found
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
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