740 research outputs found
Non-vanishing of -functions associated to cusp forms of half-integral weight
In this article, we prove non-vanishing results for -functions associated
to holomorphic cusp forms of half-integral weight on average (over an
orthogonal basis of Hecke eigenforms). This extends a result of W. Kohnen to
forms of half-integral weight.Comment: 8 pages, Accepted for publication in Oman conference proceedings
(Springer
The Saito-Kurokawa lifting and Darmon points
Let E_{/_\Q} be an elliptic curve of conductor with and let
be its associated newform of weight 2. Denote by the -adic
Hida family passing though , and by its -adic
Saito-Kurokawa lift. The -adic family of Siegel modular forms
admits a formal Fourier expansion, from which we can define a family of
normalized Fourier coefficients indexed by positive
definite symmetric half-integral matrices of size . We relate
explicitly certain global points on (coming from the theory of
Stark-Heegner points) with the values of these Fourier coefficients and of
their -adic derivatives, evaluated at weight .Comment: 14 pages. Title change
Minimally-destructive detection of magnetically-trapped atoms using frequency-synthesised light
We present a technique for atomic density measurements by the off-resonant
phase-shift induced on a two-frequency, coherently-synthesised light beam. We
have used this scheme to measure the column density of a magnetically trapped
atom cloud and to monitor oscillations of the cloud in real time by making over
a hundred non-destructive local density measurments. For measurements using
pulses of 10,000-100,000 photons lasting ~10 microsecond, the precision is
limited by statistics of the photons and the photodiode avalanche. We explore
the relationship between measurement precision and the unwanted loss of atoms
from the trap and introduce a figure of merit that characterises it. This
method can be used to probe the density of a BEC with minimal disturbance of
its phase.Comment: Submitted to New Journal of Physic
On the special values of certain L-series related to half-integral weight modular forms
Let h be a cuspidal Hecke eigenform of half-integral weight, and En/2+1/2 be Cohen’s Eisenstein series of weight n/2+1/2. For a Dirichlet character χ we define a certain linear combination R(χ)(s, h,En/+1/2) of the Rankin-Selberg convolution products of h and En/2+1/2 twisted by Dirichlet characters related with χ. We then prove a certain algebraicity result for R(χ)(l, h,En/2+1/2) with l integers
Electron microscopy analysis of femtosecond laser-assisted capsulotomy before and after lens fragmentation
Studying anterior lens capsule cutting edge profiles from femtosecond laser-assisted capsulotomy procedures performed before and after lens fragmentation. Twenty eyes (10 patients) with age-related cataract underwent femtosecond laser-assisted surgery (FLACS) using the Ziemer Z8 platform. First step of laser surgery was either capsulotomy (group first) or fragmentation (group second). One eye of each patient was assigned randomly, the second eye treated with the different sequence of procedures. After anterior capsule removal, tissue was fixed in cacodylate-buffered solution and cutting-edge profiles were analysed using scanning electron microscopy (SEM). All cases had cataract grade 2 and 3 based on LOCS III grading. SEM analysis showed more smooth edges in the first group, especially in cases with pseudoexfoliation (P = 0.037); more tags and bridges and a significant number of staggered cutting patterns (7 out of 10 cases) in the second group. All cases evolved the same microgroves with \textquotedblvalleys and mountains \textquotedbl as signs of the photodisruption process. Femtosecond laser capsulotomy should be performed before lens fragmentation minimizing the rate of cutting errors. Especially in eyes with advanced cataract, as intracapsular pressure may increase due to lens fragmentation without anterior capsular opening
Modular differential equations for characters of RCFT
We discuss methods, based on the theory of vector-valued modular forms, to
determine all modular differential equations satisfied by the conformal
characters of RCFT; these modular equations are related to the null vector
relations of the operator algebra. Besides describing effective algorithmic
procedures, we illustrate our methods on an explicit example.Comment: 13 page
Experiments on a videotape atom chip: fragmentation and transport studies
This paper reports on experiments with ultra-cold rubidium atoms confined in
microscopic magnetic traps created using a piece of periodically-magnetized
videotape mounted on an atom chip. The roughness of the confining potential is
studied with atomic clouds at temperatures of a few microKelvin and at
distances between 30 and 80 microns from the videotape-chip surface. The
inhomogeneities in the magnetic field created by the magnetized videotape close
to the central region of the chip are characterized in this way. In addition,
we demonstrate a novel transport mechanism whereby we convey cold atoms
confined in arrays of videotape magnetic micro-traps over distances as large as
~ 1 cm parallel to the chip surface. This conveying mechanism enables us to
survey the surface of the chip and observe potential-roughness effects across
different regions.Comment: 29 pages, 22 figures
A single atom detector integrated on an atom chip: fabrication, characterization and application
We describe a robust and reliable fluorescence detector for single atoms that
is fully integrated into an atom chip. The detector allows spectrally and
spatially selective detection of atoms, reaching a single atom detection
efficiency of 66%. It consists of a tapered lensed single-mode fiber for
precise delivery of excitation light and a multi-mode fiber to collect the
fluorescence. The fibers are mounted in lithographically defined holding
structures on the atom chip. Neutral 87Rb atoms propagating freely in a
magnetic guide are detected and the noise of their fluorescence emission is
analyzed. The variance of the photon distribution allows to determine the
number of detected photons / atom and from there the atom detection efficiency.
The second order intensity correlation function of the fluorescence shows
near-perfect photon anti-bunching and signs of damped Rabi-oscillations. With
simple improvements one can boost the detection efficiency to > 95%.Comment: 24 pages, 11 figure
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