Lax forms of the qq-Painlev\'e equations

All $q$-Painlev\'e equations which are obtained from the $q$-analog of the sixth Painlev\'e equation are expressed in a Lax formalism. They are characterized by the data of the associated linear $q$-difference equations. The degeneration pattern from the $q$-Painlev\'e equation of type $A_2$ is also presented.Comment: 24 page

CFT approach to the qq-Painlev\'e VI equation

Iorgov, Lisovyy, and Teschner established a connection between isomonodromic deformation of linear differential equations and Liouville conformal field theory at $c=1$. In this paper we present a $q$ analog of their construction. We show that the general solution of the $q$-Painlev\'e VI equation is a ratio of four tau functions, each of which is given by a combinatorial series arising in the AGT correspondence. We also propose conjectural bilinear equations for the tau functions.Comment: 26 page

Unified Analysis of Spin Isospin Responses of Nuclei

We investigated the Gamow-Teller (GT) strength distribution, especially the quenching with respect to the GT sum rule, and the enhancement of the pionic responses in the quasielasic scattering region, in the same theoretical framework. That is the continuum random phase approximation with the pi+rho+g' model interaction, incorporated with distorted wave impulse approximation and two-step calculations. From this analysis we searched the Landau-Migdal parameters, g'NN and g'ND, through the comparison with the experimental data of the GT strength distribution obtained at 300 MeV and the spin-longitudinal (pionic) cross sections IDq of (p,n) at 350 and 500 MeV. This comprehensive and sophisticated study gave a common set of g'NN=0.6-0.7 and g'ND=0.2-0.4, for both low and high momentum transfers.Comment: 11 pages, 4 figures, submitted to Phys. Rev.

Field induced transition of the S=1 antiferromagnetic chain with anisotropy

The ground state magnetization process of the S=1 antiferromagnetic chain with the easy-axis single-ion anisotropy described by negative $D$ is investigated. It is numerically found that a phase transition between two different gapless phases occurs at an intermediate magnetic field between the starting and saturation points of the magnetization for $-1.49<D<-0.35$. The transition is similar to the spin flopping, but it is second-order and not accompanied with any significant anomalous behaviors in the magnetization curve. We also present the phase diagrams in the m-D and H-D planes which reveal a possible re-entrant transition.Comment: 6 pages, Revtex, with 6 eps figures, to appear in Phys. Rev. B (Sep. 1

Critical exponent in the magnetization curve of quantum spin chains

The ground state magnetization curve around the critical magnetic field $H_c$ of quantum spin chains with the spin gap is investigated. We propose a size scaling method to estimate the critical exponent $\delta$ defined as $m\sim |H-H_c|^{1/\delta}$ from finite cluster calculation. The applications of the method to the S=1 antiferromagnetic chain and S=1/2 bond alternating chain lead to a common conclusion $\delta =2$. The same result is derived for both edges of the magnetization plateau of the S=3/2 antiferromagnetic chain with the single ion anisotropy.Comment: 4 pages, Revtex, with 4 eps figure

Metamagnetism of antiferromagnetic XXZ quantum spin chains

The magnetization process of the one-dimensional antiferromagnetic Heisenberg model with the Ising-like anisotropic exchange interaction is studied by the exact diagonalization technique. It results in the evidence of the first-order spin flop transition with a finite magnetization jump in the N\'eel ordered phase for $S\geq 1$. It implies that the S=1/2 chain is an exceptional case where the metamagnetic transition becomes second-order due to large quantum fluctuations.Comment: 4 pages, Revtex, with 6 eps figure

Numerical Renormalization Group Study of non-Fermi-liquid State on Dilute Uranium Systems

We investigate the non-Fermi-liquid (NFL) behavior of the impurity Anderson model (IAM) with non-Kramers doublet ground state of the f$^2$ configuration under the tetragonal crystalline electric field (CEF). The low energy spectrum is explained by a combination of the NFL and the local-Fermi-liquid parts which are independent with each other. The NFL part of the spectrum has the same form to that of two-channel-Kondo model (TCKM). We have a parameter range that the IAM shows the $- \ln T$ divergence of the magnetic susceptibility together with the positive magneto resistance. We point out a possibility that the anomalous properties of U$_x$Th$_{1-x}$Ru$_2$Si$_2$ including the decreasing resistivity with decreasing temperature can be explained by the NFL scenario of the TCKM type. We also investigate an effect of the lowering of the crystal symmetry. It breaks the NFL behavior at around the temperature, $\delta /10$, where $\delta$ is the orthorhombic CEF splitting. The NFL behavior is still expected above the temperature, $\delta/10$.Comment: 25 pages, 12 figure

Single domain YBCO/Ag bulk superconductors fabricated by seeded infiltration and growth

We have applied the seeded infiltration and growth (IG) technique to the processing of samples containing Ag in an attempt to fabricate Ag-doped Y-Ba-Cu-O (YBCO) bulk superconductors with enhanced mechanical properties. The IG technique has been used successfully to grow bulk Ag-doped YBCO superconductors of up to 25 mm in diameter in the form of single grains. The distribution of Ag in the parent Y-123 matrix fabricated by the IG technique is observed to be at least as uniform as that in samples grown by conventional top seeded melt growth (TSMG). Fine Y-211 particles were observed to be embedded within the Y-123 matrix for the IG processed samples, leading to a high critical current density, Jc, of over 70 kA/cm2 at 77.3 K in self-field. The distribution of Y-211 in the IG sample microstructure, however, is inhomogeneous, which leads to a variation in the spatial distribution of Jc throughout the bulk matrix. A maximum-trapped field of around 0.43 T at 1.2 mm above the sample surface (i.e. including 0.7 mm for the sensor mould thickness) is observed at liquid nitrogen temperature, despite the relatively small grain size of the sample (20 mm diameter × 7 mm thickness)