Abstract:
We have carried out a numerical simulation of a domain-wall model in $(2+1)$-dimensions, in the presence of a dynamical gauge field only in an extra dimension, corresponding to the weak coupling limit of a ( 2-dimensional ) physical gauge coupling. Using a quenched approximation we have investigated this model at $\beta_{s} ( = 1 / g^{2}_{s} ) =$ 0.5 ( ``symmetric'' phase), 1.0, and 5.0 (``broken'' phase), where $g_s$ is the gauge coupling constant of the extra dimension. We have found that there exists a critical value of a domain-wall mass $m_{0}^{c}$ which separates a region with a fermionic zero mode on the domain-wall from the one without it, in both symmetric and broken phases. This result suggests that the domain-wall method may work for the construction of lattice chiral gauge theories.

Abstract:
A persistent current, coupled with the spin state, of purely many-body origin is shown to exist in Nagaoka's ferromagnetic state in two dimensions (2D). This we regard as a manifestation of a gauge field, which comes from the surrounding spin configuration and acts on the hole motion, being coupled to the Aharonov-Bohm flux. This provides an example where the electron-electron interaction exerts a profound effect involving the spins in clean two-dimensional lattice systems in sharp contrast to continuum or spinless fermion systems.

Abstract:
We investigate an original domain-wall model in 4+1 dimensions numerically in the presence of U(1) dynamical gauge field only in an extra dimension, corresponding to a weak coupling limit of 4-dimensional physical gauge coupling. Using a quenched approximation we carry out numerical simulation for this model at $\beta_{s} (= 1 / g^{2}_{s}) =$ 0.29 (``symmetric'' phase) and 0.5 (``broken'' phase), where $g_s$ is the gauge coupling constant of the extra dimension. In the broken phase, we found that there exists a critical value of a domain-wall mass $m_{0}^{c}$ which separates a region with a fermionic zero mode on the domain wall from the one without it in the same case of (2+1)-dimensional model. On the other hand, in the symmetric phase, our numerical data suggest that the chiral zero modes disappear in the infinite limit of 4-dimensional volume. From these results it seems difficult to construct the U(1) lattice chiral gauge theory via an original domain-wall formulation.

Abstract:
Inspired from Sutherland's work [Phys. Rev. Lett. {\bf 74}, 816 (1995)] on detecting bound spin waves, we propose that bound electron states can be detected from the dependence of interacting electron systems to the Aharonov-Bohm flux in the `extended zone' scheme, where the electron pairing halves the original period $N_a$ flux quanta in a system of linear size $N_a$. Along with the Bethe-ansatz analysis, a numerical implementation for keeping track of the adiabatic flow of energy levels is applied to the attractive/repulsive Hubbard models and the $t-J$ ladder.

Abstract:
We carry out a numerical simulation of a domain-wall model in (4+1) dimensions, in the presence of a quenched U(1) dynamical gauge field only in an extra dimension, corresponding to the weak coupling limit of a (4-dimensional) physical gauge coupling. Our numerical data suggest that the zero mode seems absent in the symmetric phase, so that it is difficult to construct a lattice chiral gauge theory in the continuum limit.

Abstract:
A numerical scaling analysis is used to show that Nagaoka's ferromagnetic state in two-dimensional Hubbard model with one hole is supersede by an antiferromagnetic (AF) state with a discontinuous jump in the total spin due to the AF coupling as the Hubbard $U$ is made finite. The same applies to the two-hole system, which has a spiral spin structure. We can show, via the scaling, that the crossover to an AF state is a precursor of a pathological coalescence of states having the minimum spin and Nagaoka's state at $U=\infty$ in the thermodynamic limit.

Abstract:
We investigate a possibility that the rough gauge problem, which have appeared to be a main reason for failures of lattice chiral gauge theories, is cured by an asymptotic-free dynamics. Taking the domain-wall model in 2(+1) dimensions with SU(2) gauge group, we carry out the quenched simulation of gauge fields in the extra dimension. By studying fermion spectra in several volumes, we show that the chiral zero modes exist on the wall without having the spontaneous symmetry breaking thanks to the asymptotic-free dynamics. This result suggests that the rough gauge problem is solved in some class of lattice chiral fermions as well as in 4 dimensions if an asymptotic-free dynamics is incorporated.

Abstract:
HST archival FOS spectra of 40 QSOs with z <= 0.5 in the Bright Quasar Survey have been analyzed. The spectra cover the region 1800-2000 A in the QSOs' rest frames, including the Al III 1859, Si III] 1892, C III] 1909, and Fe III UV34 emission-lines. We measured the flux of these UV emission-lines, and analyzed the correlations among UV and optical (H beta, Fe II, and [O III]) emission-line properties as well as soft X-ray photon indices. We found a significant correlation between Si III]/C III] and Fe II/H beta. Si III and C III have similar ionization potentials, but Si III] has one order magnitude larger critical density than C III]. Si III]/C III] is thus a density indicator and becomes larger when density is higher. The correlation between Si III]/C III] and Fe II/H beta indicates that optical Fe II becomes strong when the density of the broad line region becomes high. Our correlation analysis shows that large Si III]/C III] associates with weak [O III] 5007, large soft X-ray photon index, and narrow H beta width as well as with large Fe II/H beta. Our results support the previous suggestions that the density of the broad line region gas and the mass accretion rate govern this correlation.

Abstract:
The proton spin structure is not understood yet and there has remained large uncertainty on Delta g, the gluon spin contribution to the proton. Double helicity asymmetry (A_LL) of pi0 production in polarized pp collisions is used to constrain Delta g. In this report, preliminary results of A_LL of pi0 in pp collisions at sqrt(s) = 62.4 GeV measured by PHENIX experiment in 2006 is presented. It can probe higer x region than the previously reported pi0 A_LL at sqrt(s) = 200 GeV thanks to the lower center of mass energy.