Semiclassical low energy scattering for one-dimensional Schr\"odinger operators with exponentially decaying potentials

We consider semiclassical Schr\"odinger operators on the real line of the form $$H(\hbar)=-\hbar^2 \frac{d^2}{dx^2}+V(\cdot;\hbar)$$ with $\hbar>0$ small. The potential $V$ is assumed to be smooth, positive and exponentially decaying towards infinity. We establish semiclassical global representations of Jost solutions $f_\pm(\cdot,E;\hbar)$ with error terms that are uniformly controlled for small $E$ and $\hbar$, and construct the scattering matrix as well as the semiclassical spectral measure associated to $H(\hbar)$. This is crucial in order to obtain decay bounds for the corresponding wave and Schr\"odinger flows. As an application we consider the wave equation on a Schwarzschild background for large angular momenta $\ell$ where the role of the small parameter $\hbar$ is played by $\ell^{-1}$. It follows from the results in this paper and \cite{DSS2}, that the decay bounds obtained in \cite{DSS1}, \cite{DS} for individual angular momenta $\ell$ can be summed to yield the sharp $t^{-3}$ decay for data without symmetry assumptions.Comment: 44 pages, minor modifications in order to match the published version, will appear in Annales Henri Poincar

Amplitude to phase conversion of InGaAs pin photo-diodes for femtosecond lasers microwave signal generation

When a photo-diode is illuminated by a pulse train from a femtosecond laser, it generates microwaves components at the harmonics of the repetition rate within its bandwidth. The phase of these components (relative to the optical pulse train) is known to be dependent on the optical energy per pulse. We present an experimental study of this dependence in InGaAs pin photo-diodes illuminated with ultra-short pulses generated by an Erbium-doped fiber based femtosecond laser. The energy to phase dependence is measured over a large range of impinging pulse energies near and above saturation for two typical detectors, commonly used in optical frequency metrology with femtosecond laser based optical frequency combs. When scanning the optical pulse energy, the coefficient which relates phase variations to energy variations is found to alternate between positive and negative values, with many (for high harmonics of the repetition rate) vanishing points. By operating the system near one of these vanishing points, the typical amplitude noise level of commercial-core fiber-based femtosecond lasers is sufficiently low to generate state-of-the-art ultra-low phase noise microwave signals, virtually immune to amplitude to phase conversion related noise.Comment: 7 pages, 6 figures, submitted to Applied Physics

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results

CMS physics technical design report: Addendum on high density QCD with heavy ions

This report presents the capabilities of the CMS experiment to explore the rich heavy-ion physics programme offered by the CERN Large Hadron Collider (LHC). The collisions of lead nuclei at energies ,will probe quark and gluon matter at unprecedented values of energy density. The prime goal of this research is to study the fundamental theory of the strong interaction - Quantum Chromodynamics (QCD) - in extreme conditions of temperature, density and parton momentum fraction (low-x). This report covers in detail the potential of CMS to carry out a series of representative Pb-Pb measurements. These include "bulk" observables, (charged hadron multiplicity, low pT inclusive hadron identified spectra and elliptic flow) which provide information on the collective properties of the system, as well as perturbative probes such as quarkonia, heavy-quarks, jets and high pT hadrons which yield "tomographic" information of the hottest and densest phases of the reaction.0info:eu-repo/semantics/publishe