SO(4) Invariant States in Quantum Cosmology

The phenomenon of linearisation instability is identified in models of quantum cosmology that are perturbations of mini-superspace models. In particular, constraints that are second order in the perturbations must be imposed on wave functions calculated in such models. It is shown explicitly that in the case of a model which is a perturbation of the mini-superspace which has $S^3$ spatial sections these constraints imply that any wave functions calculated in this model must be SO(4) invariant. (This replaces the previous corrupted version.)Comment: 15 page

On the existence of Killing vector fields

In covariant metric theories of coupled gravity-matter systems the necessary and sufficient conditions ensuring the existence of a Killing vector field are investigated. It is shown that the symmetries of initial data sets are preserved by the evolution of hyperbolic systems.Comment: 9 pages, no figure, to appear in Class. Quant. Gra

Parabolic lithium refractive optics for x rays

Excellent x-ray optics for photons at around 10 keV can be expected with lithium metal. One of the best compound refractive lens designs [Lengeler et al., J. Appl. Phys. 84, 5855 (1998)] is now produced routinely in aluminum, and more recently has been demonstrated using beryllium [M. Kuhlmann et al. (unpublished)]. Here, we report a similar refractive lens made from lithium. At 10.87 keV, this lens has a ≃2 m focal length, more than 90% peak transmission, and an average transmission of 49%. The lens shows a very useful gain of up to 40. The full widths at half maximum (FWHM) of the focus are blurred by roughly 20 μm, resulting in a horizontal and vertical FWHM of 33 and 17 μm for an image distance of 2.13 m. The lens produces speckle on the x-ray beam, which is likely due to the inhomogeneities of the lens surface: Coherent x-ray scattering is useful in understanding imperfections in x-ray optics, such as mirrors and lenses. Better molding techniques should result in improved performance and enable microbeam techniques with this type of Li lens. © 2004 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70176/2/RSINAK-75-1-37-1.pd

Experience with a fluorescence‐based beam position monitor at the APS

We have recently redesigned the first crystal mount of our cryogenically cooled monochromator to reduce its sensitivity to pressure fluctuations in the cryogenic lines feeding the Si (111) crystal. With the use of a fluorescence‐based X‐ray beam position monitor (BPM) placed 19 m away from the monochromator, much operational experience has been gained on the sensitivity of the beam position and intensity to small changes in the cooling system. In this presentation, we will describe our X‐ray BPM design and performance and will provide examples of changes that have made the beam position more stable on our beamline. One such change for example has been the top‐up operation of the Advanced Photon Source (APS), which has reduced the thermal drifts associated with the ring current decay. © 2004 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87659/2/679_1.pd

Structured matrices, continued fractions, and root localization of polynomials

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.Comment: 79 pages; new material added to the Introductio

An Imaging System for Focusing Tests of Li Multiprism X‐ray Refractive Lenses

For rapid and efficient tests of novel X‐rays optics, such as lithium‐based compound refractive lenses, we have built a fast X‐ray sensitive CCD imaging system. We report on the linearity, response and resolution of the microscope‐based imaging system. For the low magnifications used here (X2‐X10), we find that a thinly doped YAG screen has a poorer resolution than a thick YAG screen. We provide an example of its use in testing a new 2D focusing multiprism X‐ray lens. © 2004 American Institute of PhysicsPeer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87661/2/780_1.pd

Lithium metal for x-ray refractive optics

Lithium metal is the best material for refractive lenses that must focus x-rays with energies below 15 keV, but to date no lens from Li has been reported. This letter demonstrates focusing of 10 keV x-rays with a one-dimensional sawtooth lens made from Li. The lens’ theoretical gain is 4.5, with manufacturing imperfections likely responsible for the threefold gain that is observed. Despite the Li reactivity the lens is stable over months of operation if kept under vacuum. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69644/2/APPLAB-79-25-4085-1.pd

Refractive optics using lithium metal

Thanks to its low x-ray absorption, lithium should be the material of choice for x-ray refractive lenses. This article discusses some of the measurements done to verify lithium’s relevant properties. Both x-ray transmission and refraction are consistent with expectations. The lens gain suffers from broadening that is related to small-angle scattering. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69944/2/RSINAK-73-3-1492-1.pd

Supersonic strain front driven by a dense electron-hole plasma

We study coherent strain in (001) Ge generated by an ultrafast laser-initiated high density electron-hole plasma. The resultant coherent pulse is probed by time-resolved x-ray diffraction through changes in the anomalous transmission. The acoustic pulse front is driven by ambipolar diffusion of the electron-hole plasma and propagates into the crystal at supersonic speeds. Simulations of the strain including electron-phonon coupling, modified by carrier diffusion and Auger recombination, are in good agreement with the observed dynamics.Comment: 4 pages, 6 figure

The York map as a Shanmugadhasan canonical transformation in tetrad gravity and the role of non-inertial frames in the geometrical view of the gravitational field

A new parametrization of the 3-metric allows to find explicitly a York map in canonical ADM tetrad gravity, the two pairs of physical tidal degrees of freedom and 14 gauge variables. These gauge quantities (generalized inertial effects) are all configurational except the trace ${}^3K(\tau ,\vec \sigma)$ of the extrinsic curvature of the instantaneous 3-spaces $\Sigma_{\tau}$ (clock synchronization convention) of a non-inertial frame. The Dirac hamiltonian is the sum of the weak ADM energy $E_{ADM} = \int d^3\sigma {\cal E}_{ADM}(\tau ,\vec \sigma)$ (whose density is coordinate-dependent due to the inertial potentials) and of the first-class constraints. Then: i) The explicit form of the Hamilton equations for the two tidal degrees of freedom in an arbitrary gauge: a deterministic evolution can be defined only in a completely fixed gauge, i.e. in a non-inertial frame with its pattern of inertial forces. ii) A general solution of the super-momentum constraints, which shows the existence of a generalized Gribov ambiguity associated to the 3-diffeomorphism gauge group. It influences: a) the explicit form of the weak ADM energy and of the super-momentum constraint; b) the determination of the shift functions and then of the lapse one. iii) The dependence of the Hamilton equations for the two pairs of dynamical gravitational degrees of freedom (the generalized tidal effects) and for the matter, written in a completely fixed 3-orthogonal Schwinger time gauge, upon the gauge variable ${}^3K(\tau ,\vec \sigma)$, determining the convention of clock synchronization. Therefore it should be possible (for instance in the weak field limit but with relativistic motion) to try to check whether in Einstein's theory the {\it dark matter} is a gauge relativistic inertial effect induced by ${}^3K(\tau ,\vec \sigma)$.Comment: 90 page