Thermo-refractive noise in gravitational wave antennae

Thermodynamical fluctuations of temperature in mirrors of gravitational wave antennae may be transformed into additional noise not only through thermal expansion coefficient but also through temperature dependence of refraction index. The intensity of this noise is comparable with other known noises and must be taken into account in future steps of the antennas.Comment: 11 pages, 1 figure, the paper is revised as compared to one accepted in Phys.Letts.A (new numerical estimates

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.

Analysis of Parametric Oscillatory Instability in Power Recycled LIGO Interferometer

We present the analysis of a nonlinear effect of parametric oscillatory instability in power recycled LIGO interferometer with the Fabry-Perot (FP) cavities in the arms. The basis for this effect is the excitation of the additional (Stokes) optical mode and the mirror elastic mode, when the optical energy stored in the main FP cavity main mode exceeds the certain threshold and the frequencies are related so that sum of frequencies of Stokes and elastic modes are approximately equal to frequencyof main mode. The presence of anti-Stokes modes (with frequency approximately equal to sum of frequencies of main and elastic modes) can depress parametric instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric instability completely.Comment: 9 pages, 2 figures. submitted to Physics Letters

Doppler-Induced Dynamics of Fields in Fabry-Perot Cavities with Suspended Mirrors

The Doppler effect in Fabry-Perot cavities with suspended mirrors is analyzed. Intrinsically small, the Doppler shift accumulates in the cavity and becomes comparable to or greater than the line-width of the cavity if its finesse is high or its length is large. As a result, damped oscillations of the cavity field occur when one of the mirrors passes a resonance position. A formula for this transient is derived. It is shown that the frequency of the oscillations is equal to the accumulated Doppler shift and the relaxation time of the oscillations is equal to the storage time of the cavity. Comparison of the predicted and the measured Doppler shift is discussed, and application of the analytical solution for measurement of the mirror velocity is described

Thermodynamical fluctuations and photo-thermal shot noise in gravitational wave antennae

Thermodynamical fluctuations of temperature in mirrors of gravitational wave antennae are transformed through thermal expansion coefficient into additional noise. This source of noise, which may also be interpreted as fluctuations due to thermoelastic damping, may not be neglected and leads to the necessity to reexamine the choice of materials for the mirrors. Additional source of noise are fluctuations of the mirrors' surfaces caused by optical power absorbed in dielectrical reflective layers.Comment: 20 pages, 2 figure

The Hyperfine Einstein-Infeld-Hoffmann Potential

We use recently developed effective field theory techniques to calculate the third order post-Newtonian correction to the spin-spin potential between two spinning objects. This correction represents the first contribution to the spin-spin interaction due to the non-linear nature of general relativity and will play an important role in forthcoming gravity wave experiments.Comment: 4 pages, 2 figures, RevTe

Measured limits to contamination of optical surfaces by elastomers in vacuum

We have monitored the reflectivity of mirrors that were exposed to a fluoroelastomer (3M-Fluorel 2176) and a room-temperature vulcanizing silicone rubber (RTV-615) in vacuum. The 95% confidence limit on the decrease of mirror reflectivities was less than 0.35 ppm/week for Fluorel and <0.29 ppm@week for RTV-615