Lattice Dirac fermions in a non-Abelian random gauge potential: Many flavors, chiral symmetry restoration and localization

In the previous paper we studied Dirac fermions in a non-Abelian random vector potential by using lattice supersymmetry. By the lattice regularization, the system of disordered Dirac fermions is defined without any ambiguities. We showed there that at strong-disorder limit correlation function of the fermion local density of states decays algebraically at the band center. In this paper, we shall reexamine the multi-flavor or multi-species case rather in detail and argue that the correlator at the band center decays {\em exponentially} for the case of a {\em large} number of flavors. This means that a delocalization-localization phase transition occurs as the number of flavors is increased. This discussion is supported by the recent numerical studies on multi-flavor QCD at the strong-coupling limit, which shows that the phase structure of QCD drastically changes depending on the number of flavors. The above behaviour of the correlator of the random Dirac fermions is closely related with how the chiral symmetry is realized in QCD.Comment: Version appears in Mod.Phys.Lett.A17(2002)135

A theory of the electric quadrupole contribution to resonant x-ray scattering: Application to multipole ordering phases in Ce_{1-x}La_{x}B_{6}

We study the electric quadrupole (E2) contribution to resonant x-ray scattering (RXS). Under the assumption that the rotational invariance is preserved in the Hamiltonian describing the intermediate state of scattering, we derive a useful expression for the RXS amplitude. One of the advantages the derived expression possesses is the full information of the energy dependence, lacking in all the previous studies using the fast collision approximation. The expression is also helpful to classify the spectra into multipole order parameters which are brought about. The expression is suitable to investigate the RXS spectra in the localized f electron systems. We demonstrate the usefulness of the formula by calculating the RXS spectra at the Ce L_{2,3} edges in Ce_{1-x}La_{x}B_{6} on the basis of the formula. We obtain the spectra as a function of energy in agreement with the experiment of Ce_{0.7}La_{0.3}B_{6}. Analyzing the azimuthal angle dependence, we find the sixfold symmetry in the \sigma-\sigma' channel and the threefold onein the \sigma-\pi' channel not only in the antiferrooctupole (AFO) ordering phase but also in the antiferroquadrupole (AFQ) ordering phase, which behavior depends strongly on the domain distribution. The sixfold symmetry in the AFQ phase arises from the simultaneously induced hexadecapole order. Although the AFO order is plausible for phase IV in Ce_{1-x}La_{x}B_{6}, the possibility of the AFQ order may not be ruled out on the basis of azimuthal angle dependence alone.Comment: 12 pages, 6 figure

Parametric correlations versus fidelity decay: the symmetry breaking case

We derive fidelity decay and parametric energy correlations for random matrix ensembles where time--reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities can be established.Comment: 8 pages, 8 figure

Studies on X-ray Thomson Scattering from Antiferroquadrupolar Order in TmTe

We study Thomson scattering from the antiferroquadrupole ordering phase in TmTe. On the basis of the group theoretical treatment, we classify the selection rules of the scattering intensity governed by the orientation of the scattering vector G. Then, numerical verification is performed by invoking the ground states which are deduced from a J=7/2 multiplet model. The obtained intensity varies drastically depending on the magnitude and direction of G. We also calculate the scattering intensities under the applied field for H//(001) and (110). Their results behave differently when the orientation of G is changed, which is ascribed to the difference of their primary order parameters; O_{2}^{0} and O_{2}^{2} for H // (001) and (110), respectively. We make critical comparisons between our results for TmTe and the experimental ones for CeB_6. First, we assert that the intensities expected from TmTe at several forbidden Bragg spots are sufficient enough to be experimentally detected. Second, their intensities at (7/2,1/2,1/2) differ significantly and may be attributed to the difference of the order parametersbetween the \Gamma_3-type (O_{2}^{2} and O_{2}^{0}) and \Gamma_5-type (O_{yz}, O_{zx}, and O_{xy}) components, respectively.Comment: 18 pages, 3 figures, to be published in J. Phys. Soc. Jp

Spectropolarimetry of Type II supernovae (I) Sample, observational data and interstellar polarization

We investigate polarization spectra of hydrogen-rich core-collapse supernovae (Type~II SNe). The polarization signal from SNe contains two independent components: intrinsic SN polarization and interstellar polarization (ISP). From these components, we can study the SN explosion geometry and the dust properties in their host galaxies or in the Milky Way. In this first paper, using a new improved method, we investigate the properties of the ISP components of 11 well-observed Type~II SNe. As a result of our analysis, we find that 10 out of these 11 SNe showed a steady ISP component with a polarization degree $\lesssim 1.0$ \%, while one SN was consistent with zero ISP. As for the wavelength dependence, SN~2001dh (and possibly SN~2012aw) showed a non-Milky-Way-like ISP likely originating from the interstellar dust in their respective host galaxies: their polarization maxima were located at short wavelengths ($\lesssim4000$~\AA). Similar results have been obtained previously for highly reddened SNe. The majority of the SNe in our sample had too large uncertainties in the wavelength dependence of their ISP components to consider them further. Our work demonstrates that, by applying this method to a larger SN sample, further investigation of the ISP component of the SN polarization can provide new opportunities to study interstellar dust properties in external galaxies.Comment: 35 pages, 36 figures, accepted for publication in A&

Gas Metallicity of Narrow-Line Regions in Narrow-Line Seyfert 1 Galaxies and Broad-Line Seyfert 1 Galaxies

We investigate gas metallicity of narrow-line regions in narrow-line Seyfert 1 galaxies (NLS1s) and broad-line ones (BLS1s) in order to examine whether or not there is a difference in the gas metallicity between the two populations of Seyfert 1 galaxies. We apply two methods to study this issue. One is to use the emission-line flux ratio of [N II]6583/H_alpha in combination with some other optical emission-line flux ratios. This method, which has been often applied to Seyfert 2 galaxies, suggests that the gas metallicity of narrow-line regions is indistinguishable or possibly higher in BLS1s than in NLS1s. On the contrary, the other method in which only forbidden emission-line fluxes are used results in that NLS1s tend to possess metal-richer gas in the narrow-line regions than BLS1s. We point out that this inconsistency may be owing to the contamination of the broad component of permitted lines into the narrow component of ones in the first method. Since the results derived by using only forbidden emission-line fluxes do not suffer from any uncertainty of the fitting function for the broad component of Balmer lines, the results from this method are more reliable than those derived by using permitted lines. We thus conclude that the gas metallicity of narrow-line regions tends to be higher in NLS1s than in BLS1s.Comment: 12 pages including 10 figures, to appear in The Astrophysical Journa

Is there any evidence that ionised outflows quench star formation in type 1 quasars at z<1?

The aim of this paper is to test the basic model of negative AGN feedback. According to this model, once the central black hole accretes at the Eddington limit and reaches a certain critical mass, AGN driven outflows blow out gas, suppressing star formation in the host galaxy and self-regulating black hole growth. We consider a sample of 224 quasars selected from the SDSS at z<1 observed in the infrared band by Herschel. We evaluate the star formation rate in relation to several outflow signatures traced by the [OIII]4959,5007 and [OII]3726,3729 emission lines in about half of the sample with high quality spectra. Most of the quasars show asymmetric and broad wings in [OIII], which we interpret as outflow signatures. We separate the quasars in two groups, ``weakly'' and ``strongly'' outflowing, using three different criteria. When we compare the mean star formation rate in five redshift bins in the two groups, we find that the SFRs are comparable or slightly larger in the strongly outflowing quasars. We estimate the stellar mass from SED fitting and the quasars are distributed along the star formation main sequence, although with a large scatter. The scatter from this relation is uncorrelated with respect to the kinematic properties of the outflow. Moreover, for quasars dominated in the infrared by starburst or by AGN emission, we do not find any correlation between the star formation rate and the velocity of the outflow, a trend previously reported in the literature for pure starburst galaxies. We conclude that the basic AGN negative feedback scenario seems not to agree with our results. Although we use a large sample of quasars, we did not find any evidence that the star formation rate is suppressed in the presence of AGN driven outflows on large scale. A possibility is that feedback is effective over much longer timescales than those of single episodes of quasar activity.Comment: 18 pages, new version that implements the suggestions of the referee and matches the AA published versio

Abstract involutions of algebraic groups and of Kac-Moody groups

Based on the second author's thesis in this article we provide a uniform treatment of abstract involutions of algebraic groups and of Kac-Moody groups using twin buildings, RGD systems, and twisted involutions of Coxeter groups. Notably we simultaneously generalize the double coset decompositions established by Springer and by Helminck-Wang for algebraic groups and by Kac-Wang for certain Kac-Moody groups, we analyze the filtration studied by Devillers-Muhlherr in the context of arbitrary involutions, and we answer a structural question on the combinatorics of involutions of twin buildings raised by Bennett-Gramlich-Hoffman-Shpectorov