What can we learn about GW Physics with an elastic spherical antenna?

A general formalism is set up to analyse the response of an arbitrary solid elastic body to an arbitrary metric Gravitational Wave perturbation, which fully displays the details of the interaction antenna-wave. The formalism is applied to the spherical detector, whose sensitivity parameters are thereby scrutinised. A multimode transfer function is defined to study the amplitude sensitivity, and absorption cross sections are calculated for a general metric theory of GW physics. Their scaling properties are shown to be independent of the underlying theory, with interesting consequences for future detector design. The GW incidence direction deconvolution problem is also discussed, always within the context of a general metric theory of the gravitational field.Comment: 21 pages, 7 figures, REVTeX, enhanced Appendix B with numerical values and mathematical detail. See also gr-qc/000605

Vibrations and Berry Phases of Charged Buckminsterfullerene

A simple model of electron-vibron interactions in buckminsterfullerene ions is solved semiclassically. Electronic degeneracies of C$_{60}$$^{n-}$ induce dynamical Jahn-Teller distortions, which are unimodal for $n\!\ne\!3$ and bimodal for $n\!=\!3$. The quantization of motion along the Jahn-Teller manifold leads to a symmetric-top rotator Hamiltonian. I find Molecular Aharonov-Bohm effects where electronic Berry phases determine the vibrational spectra, zero point fluctuations, and electrons' pair binding energies. The latter are relevant to superconductivity in alkali-fullerenes.Comment: Latex 11 pages. IIT-00

The detection of Gravitational Waves

This chapter is concerned with the question: how do gravitational waves (GWs) interact with their detectors? It is intended to be a theory review of the fundamental concepts involved in interferometric and acoustic (Weber bar) GW antennas. In particular, the type of signal the GW deposits in the detector in each case will be assessed, as well as its intensity and deconvolution. Brief reference will also be made to detector sensitivity characterisation, including very summary data on current state of the art GW detectors.Comment: 33 pages, 12 figures, LaTeX2e, Springer style files --included. For Proceedings of the ERE-2001 Conference (Madrid, September 2001

Spherical Ornstein-Uhlenbeck processes

The paper considers random motion of a point on the surface of a sphere, in the case where the angular velocity is determined by an Ornstein-Uhlenbeck process. The solution is fully characterised by only one dimensionless number, the persistence angle, which is the typical angle of rotation during the correlation time of the angular velocity. We first show that the two-dimensional case is exactly solvable. When the persistence angle is large, a series for the correlation function has the surprising property that its sum varies much more slowly than any of its individual terms. In three dimensions we obtain asymptotic forms for the correlation function, in the limits where the persistence angle is very small and very large. The latter case exhibits a complicated transient, followed by a much slower exponential decay. The decay rate is determined by the solution of a radial Schrödinger equation in which the angular momentum quantum number takes an irrational value, namely j=½ (√17-1). Possible applications of the model to objects tumbling in a turbulent environment are discussed