Local RBF approximation for scattered data fitting with bivariate splines

In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given

Cosmological Perturbations of Quantum-Mechanical Origin and Anisotropy of the Microwave Background

Cosmological perturbations generated quantum-mechanically (as a particular case, during inflation) possess statistical properties of squeezed quantum states. The power spectra of the perturbations are modulated and the angular distribution of the produced temperature fluctuations of the CMBR is quite specific. An exact formula is derived for the angular correlation function of the temperature fluctuations caused by squeezed gravitational waves. The predicted angular pattern can, in principle, be revealed by the COBE-type observations.Comment: 9 pages, WUGRAV-92-17 Accepted for Publication in Phys. Rev. Letters (1993

On Bures fidelity of displaced squeezed thermal states

Fidelity plays a key role in quantum information and communication theory. Fidelity can be interpreted as the probability that a decoded message possesses the same information content as the message prior to coding and transmission. In this paper, we give a formula of Bures fidelity for displaced squeezed thermal states directly by the displacement and squeezing parameters and birefly discuss how the results can apply to quantum information theory.Comment: 10 pages with RevTex require

Ultra-high brilliance multi-MeV γ\gamma-ray beam from non-linear Thomson scattering

We report on the generation of a narrow divergence ($\theta\approx 2.5$ mrad), multi-MeV ($E_\text{MAX} = 18$ MeV) and ultra-high brilliance ($\approx 2\times10^{19}$ photons s$^{-1}$ mm$^{-2}$ mrad $^{-2}$ 0.1\% BW) $\gamma$-ray beam from the scattering of an ultra-relativistic laser-wakefield accelerated electron beam in the field of a relativistically intense laser (dimensionless amplitude $a_0\approx2$). The spectrum of the generated $\gamma$-ray beam is measured, with MeV resolution, seamlessly from 6 MeV to 18 MeV, giving clear evidence of the onset of non-linear Thomson scattering. The photon source has the highest brilliance in the multi-MeV regime ever reported in the literature

Geometric Phase, Hannay's Angle, and an Exact Action Variable

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase space after a time evolution. The condition for the existence of Hannay's angle turns out to be identical to that for the existence of a complete set of (quasi)periodic wave functions. Hannay's angle is calculated, and it is shown that Berry's relation of semiclassical origin on geometric phase and Hannay's angle is exact for the cases considered.Comment: Submitted to Phys. Rev. Lett. (revised version

Two Mode Quantum Systems: Invariant Classification of Squeezing Transformations and Squeezed States

A general analysis of squeezing transformations for two mode systems is given based on the four dimensional real symplectic group Sp(4,\Re)\/. Within the framework of the unitary metaplectic representation of this group, a distinction between compact photon number conserving and noncompact photon number nonconserving squeezing transformations is made. We exploit the Sp(4,\Re)-SO(3,2)\/ local isomorphism and the U(2)\/ invariant squeezing criterion to divide the set of all squeezing transformations into a two parameter family of distinct equivalence classes with representative elements chosen for each class. Familiar two mode squeezing transformations in the literature are recognized in our framework and seen to form a set of measure zero. Examples of squeezed coherent and thermal states are worked out. The need to extend the heterodyne detection scheme to encompass all of U(2)\/ is emphasized, and known experimental situations where all U(2)\/ elements can be reproduced are briefly described.Comment: Revtex 37 pages, Latex figures include

Vacuum fluctuations and the conditional homodyne detection of squeezed light

Conditional homodyne detection of quadrature squeezing is compared with standard nonconditional detection. Whereas the latter identifies nonclassicality in a quantitative way, as a reduction of the noise power below the shot noise level, conditional detection makes a qualitative distinction between vacuum state squeezing and squeezed classical noise. Implications of this comparison for the realistic interpretation of vacuum fluctuations (stochastic electrodynamics) are discussed.Comment: 14 pages, 7 figures, to appear in J. Opt. B: Quantum Semiclass. Op

On-ground tests of LISA PathFinder thermal diagnostics system

Thermal conditions in the LTP, the LISA Technology Package, are required to be very stable, and in such environment precision temperature measurements are also required for various diagnostics objectives. A sensitive temperature gauging system for the LTP is being developed at IEEC, which includes a set of thermistors and associated electronics. In this paper we discuss the derived requirements applying to the temperature sensing system, and address the problem of how to create in the laboratory a thermally quiet environment, suitable to perform meaningful on-ground tests of the system. The concept is a two layer spherical body, with a central aluminium core for sensor implantation surrounded by a layer of polyurethane. We construct the insulator transfer function, which relates the temperature at the core with the laboratory ambient temperature, and evaluate the losses caused by heat leakage through connecting wires. The results of the analysis indicate that, in spite of the very demanding stability conditions, a sphere of outer diameter of the order one metre is sufficient. We provide experimental evidence confirming the model predictions.Comment: 18 pages, 5 figures, LaTeX2e (compile with pdflatex), sumbitted to CQG. This paper is a significant extension of gr-qc/060109