Compact Toeplitz operators with continuous symbols on weighted Bergman spaces

Let L (n,dud0/21r) be a complete weighted Bergman space on the open unit disc n where du is a positive finite Borel measure on [O, 1). We show the following : When cp is a continuous function on the closed unit disc D, T</J is compact if and only if cp = 0 on an

Mineralogical aspects of interstratified chlorite-smectite associated with epithermal ore veins: A case study of the Todoroki Au-Ag ore deposit, Japan

Chlorite (C)-corrensite (Co)-smectite (S) seriesminerals occur as vein constituents in the two epithermal ore veins, the Chuetsu and Shuetsu veins of the Todoroki Au-Ag deposit. The characteristics of the C-Co-S seriesminerals indicate that the clays may be products of direct precipitation from hydrothermal fluids and subsequent mineralogical transformations during and/or after vein formation. The minerals from the Chuetsu vein are characterized by 'monomineralic' corrensite showing an extensive distribution throughout the vein, and trioctahedral smectite occurring locally. The Shuetsu vein minerals are characterized by C-Co series minerals which can be divided into three different types: a I type including discrete chlorite with minor amounts of S layers, a II type comprising interstratified C/Co and discrete chlorite, and a III type characterized by segregation structures of C and Co layers. The C-Co series minerals show slightly different spatial distributions in the Shuetsu vein. Different epithermal environments during the vein formations and possible kinetic effects may have played a role in the formation and conversion of Co-C series at the Shuetsu vein and S-Co series at the Chuetsu vein

Dephasing in matter-wave interferometry

We review different attempts to show the decoherence process in double-slit-like experiments both for charged particles (electrons) and neutral particles with permanent dipole moments. Interference is studied when electrons or atomic systems are coupled to classical or quantum electromagnetic fields. The interaction between the particles and time-dependent fields induces a time-varying Aharonov phase. Averaging over the phase generates a suppression of fringe visibility in the interference pattern. We show that, for suitable experimental conditions, the loss of contrast for dipoles can be almost as large as the corresponding one for coherent electrons and therefore, be observed. We analyze different trajectories in order to show the dependence of the decoherence factor with the velocity of the particles.Comment: 9 pages, 1 eps-figure. To appear in J. Phys. A: Math. Ge

Constraint propagation in the family of ADM systems

The current important issue in numerical relativity is to determine which formulation of the Einstein equations provides us with stable and accurate simulations. Based on our previous work on "asymptotically constrained" systems, we here present constraint propagation equations and their eigenvalues for the Arnowitt-Deser-Misner (ADM) evolution equations with additional constraint terms (adjusted terms) on the right hand side. We conjecture that the system is robust against violation of constraints if the amplification factors (eigenvalues of Fourier-component of the constraint propagation equations) are negative or pure-imaginary. We show such a system can be obtained by choosing multipliers of adjusted terms. Our discussion covers Detweiler's proposal (1987) and Frittelli's analysis (1997), and we also mention the so-called conformal-traceless ADM systems.Comment: 11 pages, RevTeX, 2 eps figure

Adjusted ADM systems and their expected stability properties: constraint propagation analysis in Schwarzschild spacetime

In order to find a way to have a better formulation for numerical evolution of the Einstein equations, we study the propagation equations of the constraints based on the Arnowitt-Deser-Misner formulation. By adjusting constraint terms in the evolution equations, we try to construct an "asymptotically constrained system" which is expected to be robust against violation of the constraints, and to enable a long-term stable and accurate numerical simulation. We first provide useful expressions for analyzing constraint propagation in a general spacetime, then apply it to Schwarzschild spacetime. We search when and where the negative real or non-zero imaginary eigenvalues of the homogenized constraint propagation matrix appear, and how they depend on the choice of coordinate system and adjustments. Our analysis includes the proposal of Detweiler (1987), which is still the best one according to our conjecture but has a growing mode of error near the horizon. Some examples are snapshots of a maximally sliced Schwarzschild black hole. The predictions here may help the community to make further improvements.Comment: 23 pages, RevTeX4, many figures. Revised version. Added subtitle, reduced figures, rephrased introduction, and a native checked. :-

Sensitivity of the Fe Kα\alpha Compton shoulder to the geometry and variability of the X-ray illumination of cosmic objects

In an X-ray reflection spectrum, a tail-like spectral feature generated via Compton downscattering, known as a Compton shoulder (CS), appears at the low-energy side of the iron K$\alpha$ line. Despite its great diagnostic potential, its use as a spectral probe of the reflector has been seriously limited due to observational difficulties and modelling complexities. We revisit the basic nature of the CS by systematic investigation into its dependence on spatial and temporal parameters. The calculations are performed by Monte Carlo simulations for sphere and slab geometries. The dependence is obtained in a two-dimensional space of column density and metal abundance, demonstrating that the CS solves parameter degeneration between them which was seen in conventional spectral analysis using photoelectric absorption and fluorescence lines. Unlike the iron line, the CS does not suffer from any observational dependence on the spectral hardness. The CS profile is highly dependent on the inclination angle of the slab geometry unless the slab is Compton-thick, and the time evolution of the CS is shown to be useful to constrain temporal information on the source if the intrinsic radiation is variable. We also discuss how atomic binding of the scattering electrons in cold matter blurs the CS profile, finding that the effect is practically similar to thermal broadening in a plasma with a moderate temperature of ~5 eV. Spectral diagnostics using the CS is demonstrated with grating data of X-ray binary GX 301−2, and will be available in future with high-resolution spectra of active galactic nuclei obtained by microcalorimeters.JSPS KAKENHI (Grant IDs: 24740190, 24105007), Advanced Leading graduate school for Photon Science (ALPS