On the Correlations between Galaxy Properties and Supermassive Black Hole Mass

We use a large sample of upper limits and accurate estimates of supermassive black holes masses coupled with libraries of host galaxy velocity dispersions, rotational velocities and photometric parameters extracted from Sloan Digital Sky Survey i-band images to establish correlations between the SMBH and host galaxy parameters. We test whether the mass of the black hole, MBH, is fundamentally driven by either local or global galaxy properties. We explore correlations between MBH and stellar velocity dispersion sigma, bulge luminosity, bulge mass Sersic index, bulge mean effective surface brightness, luminosity of the galaxy, galaxy stellar mass, maximum circular velocity Vc, galaxy dynamical and effective masses. We verify the tightness of the MBH-sigma relation and find that correlations with other galaxy parameters do not yield tighter trends. We do not find differences in the MBH-sigma relation of barred and unbarred galaxies. The MBH-sigma relation of pseudo-bulges is also coarser and has a different slope than that involving classical bulges. The MBH-bulge mass is not as tight as the MBH-sigma relation, despite the bulge mass proving to be a better proxy of MBH than bulge luminosity. We find a rather poor correlation between MBH and Sersic index suggesting that MBH is not related to the bulge light concentration. The correlations between MBH and galaxy luminosity or mass are not a marked improvement over the MBH sigma relation. If Vc is a proxy for the dark matter halo mass, the large scatter of the MBH-Vc relation then suggests that MBH is more coupled to the baryonic rather than the dark matter. We have tested the need for a third parameter in the MBH scaling relations, through various linear correlations with bulge and galaxy parameters, only to confirm that the fundamental plane of the SMBH is mainly driven by sigma, with a small tilt due to the effective radius. (Abridged)Comment: 32 pages, 18 figures, 6 tables, accepted for publication in MNRA

Electric field driven quantum phase transition between band insulator and topological insulator

We demonstrate theoretically that electric field can drive a quantum phase transition between band insulator to topological insulator in CdTe/HgCdTe/CdTe quantum wells. The numerical results suggest that the electric field could be used as a switch to turn on or off the topological insulator phase, and temperature can affect significantly the phase diagram for different gate voltage and compositions. Our theoretical results provide us an efficient way to manipulate the quantum phase of HgTe quantum wells.Comment: 4 pages, 4 figure

Differential Forms and Wave Equations for General Relativity

Recently, Choquet-Bruhat and York and Abrahams, Anderson, Choquet-Bruhat, and York (AACY) have cast the 3+1 evolution equations of general relativity in gauge-covariant and causal ``first-order symmetric hyperbolic form,'' thereby cleanly separating physical from gauge degrees of freedom in the Cauchy problem for general relativity. A key ingredient in their construction is a certain wave equation which governs the light-speed propagation of the extrinsic curvature tensor. Along a similar line, we construct a related wave equation which, as the key equation in a system, describes vacuum general relativity. Whereas the approach of AACY is based on tensor-index methods, the present formulation is written solely in the language of differential forms. Our approach starts with Sparling's tetrad-dependent differential forms, and our wave equation governs the propagation of Sparling's 2-form, which in the ``time-gauge'' is built linearly from the ``extrinsic curvature 1-form.'' The tensor-index version of our wave equation describes the propagation of (what is essentially) the Arnowitt-Deser-Misner gravitational momentum.Comment: REVTeX, 26 pages, no figures, 1 macr

A pseudopotential study of electron-hole excitations in colloidal, free-standing InAs quantum dots

Excitonic spectra are calculated for free-standing, surface passivated InAs quantum dots using atomic pseudopotentials for the single-particle states and screened Coulomb interactions for the two-body terms. We present an analysis of the single particle states involved in each excitation in terms of their angular momenta and Bloch-wave parentage. We find that (i) in agreement with other pseudopotential studies of CdSe and InP quantum dots, but in contrast to k.p calculations, dot states wavefunction exhibit strong odd-even angular momentum envelope function mixing (e.g. $s$ with $p$) and large valence-conduction coupling. (ii) While the pseudopotential approach produced very good agreement with experiment for free-standing, colloidal CdSe and InP dots, and for self-assembled (GaAs-embedded) InAs dots, here the predicted spectrum does {\em not} agree well with the measured (ensemble average over dot sizes) spectra. (1) Our calculated excitonic gap is larger than the PL measure one, and (2) while the spacing between the lowest excitons is reproduced, the spacings between higher excitons is not fit well. Discrepancy (1) could result from surface states emission. As for (2), agreement is improved when account is taken of the finite size distribution in the experimental data. (iii) We find that the single particle gap scales as $R^{-1.01}$ (not $R^{-2}$), that the screened (unscreened) electron-hole Coulomb interaction scales as $R^{-1.79}$ ($R^{-0.7}$), and that the eccitonic gap sclaes as $R^{-0.9}$. These scaling laws are different from those expected from simple models.Comment: 12 postscript figure

Endogenous Income Distribution with Product Obsolescence

Wage inequality in U. S. and UK has increased over the past 25 years. Paradoxically, skilled labor supply has also increased in both countries. This paper develops the dynamic general equilibrium model of product innovation with product obsolescence. We develop a model to provide an explanation of inequality phenomena between skilled and unskilled labor by the channel of innovation and market structure. This paper builds on the dynamic general equilibrium model of product innovation and incorporates overhead cost of the production of intermediate goods to capture endogenous growth rate of innovation, hazard rate, product life cycle and inequality.wage inequality, skilled and unskilled labor, product innovation, general equilibrium

Resonant acousto-optics in the terahertz range: TO-phonon polaritons driven by an ultrasonic wave

The resonant acousto-optic effect is studied both analytically and numerically in the terahertz range where the transverse-optical (TO) phonons play the role of a mediator which strongly couples the ultrasound and light fields. A propagating acoustic wave interacts with the TO phonons via anharmonic channels and opens band gaps in the TO-phonon polariton energy dispersion that results in pronounced Bragg scattering and reflection of the incoming light. The separation in frequency of different Bragg replicas, which is at the heart of acousto-optics, allows us to study the resonant acousto-optic effect in the most simple and efficient geometry of collinear propagation of electromagnetic and ultrasonic waves. The acoustically induced energy gaps, Bragg reflection spectra, and the spatial distribution of the electric field and polarization are calculated for CuCl parameters, in a wide range of frequencies and intensities of the pumping acoustic wave. Our results show drastic changes in terahertz spectra of semiconductor crystals that opens the way for efficient and accessible manipulation of their infrared properties, by tuning the parameters of the acoustic wave.Comment: 20 pages, 14 figure