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

Geodesic knots in cusped hyperbolic 3-manifolds

We consider the existence of simple closed geodesics or "geodesic knots" in finite volume orientable hyperbolic 3-manifolds. Previous results show that at least one geodesic knot always exists [Bull. London Math. Soc. 31(1) (1999) 81-86], and that certain arithmetic manifolds contain infinitely many geodesic knots [J. Diff. Geom. 38 (1993) 545-558], [Experimental Mathematics 10(3) (2001) 419-436]. In this paper we show that all cusped orientable finite volume hyperbolic 3-manifolds contain infinitely many geodesic knots. Our proof is constructive, and the infinite family of geodesic knots produced approach a limiting infinite simple geodesic in the manifold.Comment: This is the version published by Algebraic & Geometric Topology on 19 November 200

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.

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

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

Frustration-induced eta inversion in the S=1/2 bond-alternating spin chain

We study the frustration-induced enhancement of the incommensurate correlation for a bond-alternating quantum spin chain in a magnetic field, which is associated with a quasi-one-dimensional organic compound F5PNN. We investigate the temperature dependence of the staggered susceptibilities by using the density matrix renormalization group, and then find that the incommensurate correlation becomes dominant in a certain range of the magnetic field. We also discuss the mechanism of this enhancement on the basis of the mapping to the effective S=1/2 XXZ chain and a possibility of the field-induced incommensurate long range order.Comment: 4 pages, 5 figures, replaced with revised version accepted to PR

Field-induced long-range order in the S=1 antiferromagnetic chain

The quasi-one dimensional S=1 antiferromagnet in magnetic field H is investigated with the exact diagonalization of finite chains and the mean field approximation for the interchain interaction. In the presence of the single-ion anisotropy D, the full phase diagram in the $HT$ plane is presented for H \parallel D and H \perp D. The shape of the field-induced long-range ordered phase is revealed to be quite different between the two cases, as observed in the recent experiment of NDMAP. The estimated ratio of the interchain and intrachain couplings of NDMAP (J'/J ~ 10^{-3}) is consistent with the neutron scattering measurement.Comment: 4 pages, Revtex, with 6 eps 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)