The one-dimensional Coulomb Problem

One-dimensional scattering by a Coulomb potential V(x)=lambda/|x| is studied for both repulsive (c>0) and attractive (c<0) cases. Two methods of regularizing the singularity at x=0 are used, yielding the same conclusion, namely, that the transmission vanishes. For an attractive potential (c<0), two groups of bound states are found. The first one consists of "regular" (Rydberg) bound states, respecting standard orthogonality relations. The second set consists of "anomalous"} bound states (in a sense to be clarified), which always relax as coherent states.Comment: 29 pages, accepted in J. Phys.

Magnetic field induced singlet - triplet phase transition in quasi one-dimensional organic superconductors

We propose a theoretical model of quasi-one-dimensional superconductors, with attractive electron-electron interactions dominant in the singlet d-wave channel and sub-dominant in the p-wave channel. We discuss, in the mean field approximation, the effect of a magnetic field applied perpendicularly to the direction of the lowest conductivity. The lowest free energy phase corresponds to a singlet d-wave symmetry in low fields, but to a triplet symmetry in high fields. A first order singlet-triplet phase transition is expected at moderate applied fields of a few teslas. We propose to ascribe the recent critical field and NMR experimental data, observed in superconducting (TMTSF)2ClO4 to such an effect.Comment: 6 pages, 2 figures, accepted in EP

Charge and Spin Density Waves observed through their spatial fluctuations by coherent and simultaneous X-ray diffraction

Spatial uctuations of spin density wave (SDW) and charge density wave (CDW) in chromium have been compared by combining coherent and simultaneous X-ray diffraction experiments. Despite their close relationship, spatial fluctuations of the spin and of the charge density waves display a very different behavior: the satellite reflection associated to the charge density displays speckles while the spin one displays an impressive long-range order. This observation is hardly compatible with the commonly accepted magneto-elastic origin of CDW in chromium and is more consistent with a purely electronic scenario where CDW is the second harmonic of SDW. A BCS model taking into account a second order nesting predicts correctly the existence of a CDW and explains why the CDW is more sensitive to punctual defects.Comment: 4 pages, 4 figures; Accepted in Phys. Rev.

Suspensions Thermal Noise in the LIGO Gravitational Wave Detector

We present a calculation of the maximum sensitivity achievable by the LIGO Gravitational wave detector in construction, due to limiting thermal noise of its suspensions. We present a method to calculate thermal noise that allows the prediction of the suspension thermal noise in all its 6 degrees of freedom, from the energy dissipation due to the elasticity of the suspension wires. We show how this approach encompasses and explains previous ways to approximate the thermal noise limit in gravitational waver detectors. We show how this approach can be extended to more complicated suspensions to be used in future LIGO detectors.Comment: 28 pages, 13 figure

Gravitational Wave Astrometry for Rapidly Rotating Neutron Stars and Estimation of Their Distances

We discuss an astrometric timing effect on data analysis of continuous gravitational waves from rapidly rotating isolated neutron stars. Special attention is directed to the possibility of determining their distances by measuring the curvature of the wave fronts. We predict that if continuous gravitational waves from an unknown neutron star with a stable rotation are detected around 1kHz within 1/3yr by initial LIGO detectors and the ellipticity parameter epsilon is smaller than 10^{-6}, the distance r to the source can be estimated with relative error \Delta r/r of \sim 10% by using the broad band configuration of advanced LIGO detectors over 3 years. By combining the observed amplitude of the waves with the estimated distance, information on the parameter $\epsilon$ can be obtained purely through gravitational wave measurements.Comment: 6 pages, 1 figure, to appear in PR

Alignment procedure for the VIRGO Interferometer: experimental results from the Frascati prototype

A small fixed-mirror Michelson interferometer has been built in Frascati to experimentally study the alignment method that has been suggested for VIRGO. The experimental results fully confirm the adequacy of the method. The minimum angular misalignment that can be detected in the present set-up is 10 nrad/sqrt{Hz}Comment: 10 pages, LaTex2e, 4 figures, 5 tables. Submitted to Phys. Lett.

Constraint Likelihood analysis for a network of gravitational wave detectors

We propose a coherent method for the detection and reconstruction of gravitational wave signals for a network of interferometric detectors. The method is derived using the likelihood functional for unknown signal waveforms. In the standard approach, the global maximum of the likelihood over the space of waveforms is used as the detection statistic. We identify a problem with this approach. In the case of an aligned pair of detectors, the detection statistic depends on the cross-correlation between the detectors as expected, but this dependence dissappears even for infinitesimally small misalignments. We solve the problem by applying constraints on thelikelihood functional and obtain a new class of statistics. The resulting method can be applied to the data from a network consisting of any number of detectors with arbitrary detector orientations. The method allows us reconstruction of the source coordinates and the waveforms of two polarization components of a gravitational wave. We study the performance of the method with numerical simulation and find the reconstruction of the source coordinates to be more accurate than in the standard approach.Comment: 13 pages, 6 figure

A phenomenological description of quantum-gravity-induced space-time noise

I propose a phenomenological description of space-time foam and discuss the experimental limits that are within reach of forthcoming experiments.Comment: 10 pages, LaTex, 1 figure. Short paper, omitting most technical details. More detailed analysis was reported in gr-qc/010400

Toward Quantum-Limited Position Measurements Using Optically Levitated Microspheres

We describe the use of optically levitated microspheres as test masses in experiments aimed at reaching and potentially exceeding the standard quantum limit for position measurements. Optically levitated microspheres have low mass and are essentially free of suspension thermal noise, making them well suited for reaching the quantum regime. Table-top experiments using microspheres can bridge the gap between quantum-limited position measurements of single atoms and measurements with multi-kg test masses like those being used in interferometric gravitational wave detectors