Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities

We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal potentials related to the weights in the above mentioned inequalities.Comment: 16 page

Spectroscopic confirmation of a cluster of galaxies at z=1 in the field of the gravitational lens MG2016+112

We present new optical data on the cluster AX J2019+1127 identified by the X-ray satellite ASCA at z\sim 1 (Hattori et al. 1997). The data suggest the presence of a high-redshift cluster of galaxies responsible for the large separation triple quasar MG2016+112. Our deep photometry reveals an excess of z\sim 1 galaxy candidates, as already suspected by Benitez et al. (1999). Our spectroscopic survey of 44 objects in the field shows an excess of 6 red galaxies securely identified at z \sim 1, with a mean redshift of z =1.005 +/- 0.002. We estimate a velocity dispersion of \sigma = 771 (+430/-160) km s(-1) based on these 6 galaxies and a V-band mass-to-light ratio of 215 (+308/-77) h_50 M/L_sol. Our observations thus confirm the existence of a massive structure acting as the lens, which explains the unusual configuration of the triple quasar. Hence, there is no more need to invoke the existence of a ``dark cluster'' to understand this lens system.Comment: 8 pages, 4 figures, uses aa.cls, accepted to Astronomy and Astrophysics with minor change

Quantum fluctuation induced ordered phase in the Blume-Capel model

We consider the Blume-Capel model with the quantum tunneling between the excited states. We find a magnetically ordered phase transition induced by quantum fluctuation in a model. The model has no phase transition in the corresponding classical case. Usually, quantum fluctuation breaks ordered phase as in the case of the transverse field Ising model. However, in present case, an ordered phase is induced by quantum fluctuation. Moreover, we find a phase transition between a quantum paramagnetic phase and a classical diamagnetic phase at zero temperature. We study the properties of the phase transition by using a mean field approximation (MFA), and then, by a quantum Monte Carlo method to confirm the result of the MFA.Comment: 7 pages, 6 figures, corrected some typo

The SBF Survey of Galaxy Distances. II. Local and Large-Scale Flows

We present analysis of local large scale flows using the Surface Brightness Fluctuation (SBF) Survey for the distances to 300 early-type galaxies. Our models of the distribution function of mean velocity and velocity dispersion at each point in space include a uniform thermal velocity dispersion and spherical attractors whose position, amplitude, and radial shape are free to vary. Our fitting procedure performs a maximum likelihood fit of the model to the observations. We obtain a Hubble constant of Ho = 77 +/- 4 +/- 7 km/s/Mpc, but a uniform Hubble flow is not acceptable fit to the data. Inclusion of two attractors, one of whose fit location coincides with the Virgo cluster and the other whose fit location is slightly beyond the Centaurus clusters nearly explain the peculiar velocities, but the quality of the fit can be further improved by the addition of a quadrupole correction to the Hubble flow. Although the dipole and quadrupole may be genuine manifestations of more distant density fluctuations, we find evidence that they are more likely due to non-spherical attractors. We find no evidence for bulk flows which include our entire survey volume (R < 3000 km/s); our volume is at rest with respect to the CMB. The fits to the attractors both have isothermal radial profiles (v ~ 1/r) over a range of overdensity between about 10 and 1, but fall off more steeply at larger radius. The best fit value for the small scale, cosmic thermal velocity is 180 +/- 14 km/s.Comment: 37 pages, AASTeX Latex, including 30 Postscript figures, submitted to Astrophysical Journal, July 2, 199

Magnetic aftereffect in rare earth-iron-boron magnets

The temperature dependences of the aftereffect coefficient Sv and the coercive force iHc have been measured from 4.2K to 300K on two specimens prepared from sintered magnets of Pr8Y7Fe77B8(sintered at 1060°C and 1100°C). The latter has higher maximum energy products. The Sv values of both have a maximum at 60K and 150K respectively. This is a new behavior which can not be explained by any theory proposed until now. </p

Origin of the Verwey transition in magnetite: Group theory, electronic structure, and lattice dynamics study

The Verwey phase transition in magnetite has been analyzed using the group theory methods. It is found that two order parameters with the symmetries $X_3$ and $\Delta_5$ induce the structural transformation from the high-temperature cubic to the low-temperature monoclinic phase. The coupling between the order parameters is described by the Landau free energy functional. The electronic and crystal structure for the cubic and monoclinic phases were optimized using the {\it ab initio} density functional method. The electronic structure calculations were performed within the generalized gradient approximation including the on-site interactions between 3d electrons at iron ions -- the Coulomb element $U$ and Hund's exchange $J$. Only when these local interactions are taken into account, the phonon dispersion curves, obtained by the direct method for the cubic phase, reproduce the experimental data. It is shown that the interplay of local electron interations and the coupling to the lattice drives the phonon order parameters and is responsible for the opening of the gap at the Fermi energy. Thus, it is found that the metal-insulator transition in magnetite is promoted by local electron interactions, which significantly amplify the electron-phonon interaction and stabilize weak charge order coexisting with orbital order of the occupied $t_{2g}$ states at Fe ions. This provides a scenario to understand the fundamental problem of the origin of the Verwey transition in magnetite.Comment: 17 pages, 5 figures, 8 tables. Accepted version to be published in Phys. Rev.

An Electron Spin Resonance Selection Rule for Spin-Gapped Systems

The direct electron spin resonance (ESR) absorption between a singlet ground state and the triplet excited states of spin gap systems is investigated. Such an absorption, which is forbidden by the conservation of the total spin quantum number in isotropic Hamiltonians, is allowed by the Dzyaloshinskii-Moriya interaction. We show a selection rule in the presence of this interaction, using the exact numerical diagonalization of the finite cluster of the quasi-one-dimensional bond-alternating spin system. The selection rule is also modified into a suitable form in order to interpret recent experimental results on CuGeO$_3$ and NaV$_2$O$_5$.Comment: 5 pages, Revtex, with 6 eps figures, to appear in J. Phys. Soc. Jpn. Vol. 69 No. 11 (2000

Free Fermions and Thermal AdS/CFT

The dynamics of finite temperature U(N) gauge theories on $S^3$ can be described, at weak coupling, by an effective unitary matrix model. Here we present an exact solution to these models, for any value of $N$, in terms of a sum over representations. Taking the large $N$ limit of this solution provides a new perspective on the deconfinement transition which is supposed to be dual to the Hawking-Page transition. The large $N$ phase transition manifests itself here in a manner similar to the Douglas-Kazakov phase transition in 2d Yang-Mills theory. We carry out a complete analysis of the saddle representation in the simplest case involving only the order parameter ${\rm Tr}U$. We find that the saddle points corresponding to thermal $AdS$, the small black hole and the large black hole can all be described in terms of free fermions. They all admit a simple phase space description {\it a la} the BPS geometries of Lin, Lunin and Maldacena.Comment: (0+34) pages and 9 figures, v2 references adde

Intercalation and Staging Behavior in Super-Oxygenated La2CuO4+δLa_2CuO_{4 + \delta}

A high temperature electrochemical oxidation process has been used to produce large single crystals of $La_2CuO_{4 + \delta}$ suitable for neutron scattering experiments. Below room temperature the oxygen-rich phases have structural superlattice scattering peaks which indicate new periodicities ranging from 2 to 6.6 layers perpendicular to the copper oxide planes. A model structure originally proposed for $La_2NiO_{4 + \delta}$ can account for the superlattice peaks as a result of anti-phase domain boundaries between different tilt directions of the CuO$_6$ octahedra. Within this model, the changes in CuO$_6$ tilt directions are induced by segregated layers of interstitial oxygen which order in a manner similar to intercalants in graphite. This structural model thus clarifies previous work and establishes $La_2CuO_{4 + \delta}$ as a unique lamellar superconducting system with annealed disorder.Comment: 23 pages, latex, 6 figures (not including Figures 2 & 7 and Table 1 which were not submitted but are available upon request to the Authors at: [email protected]