Toda Lattice and Tomimatsu-Sato Solutions

We discuss an analytic proof of a conjecture (Nakamura) that solutions of Toda molecule equation give those of Ernst equation giving Tomimatsu-Sato solutions of Einstein equation. Using Pfaffian identities it is shown for Weyl solutions completely and for generic cases partially.Comment: LaTeX 8 page

A Characterization of Discrete Time Soliton Equations

We propose a method to characterize discrete time evolution equations, which generalize discrete time soliton equations, including the $q$-difference Painlev\'e IV equations discussed recently by Kajiwara, Noumi and Yamada.Comment: 13 page

Novel in-gap spin state in Zn-doped La_1.85Sr_0.15CuO_4

Low-energy spin excitations of La1.85Sr0.15Cu1-yZnyO4 were studied by neutron scattering. In y=0.004, the incommensurate magnetic peaks show a well defined ``spin gap'' below Tc. The magnetic signals at omega=3 meV decrease below Tc=27 K for y=0.008, also suggesting the gap opening. At lower temperatures, however, the signal increases again, implying a novel in-gap spin state. In y=0.017, the spin gap vanishes and elastic magnetic peaks appear. These results clarify that doped Zn impurities induce the novel in-gap state, which becomes larger and more static with increasing Zn.Comment: 4 pages, 4 figure

L1521E: A Starless Core in the Early Evolutionary Stage ?

We have studied the physical and chemical properties of a quiescent starless core L1521E with various molecular lines. It is found that there exists a compact dense core traced by the H^13CO^+, HN^13C, CCS, and HC_3N lines; their distributions have a single peak at the same position. The core radius is as small as 0.031 pc, whereas the H_2 density at the peak position is as high as (1.3-5.6)times10^5 cm^-3. Although the density is high enough to excite the inversion transitions of NH_3, these lines are found to be very faint in L1521E. The distributions of NH_3 and CCS seem to be different from those of well-studied starless cores, L1498 and L1544, where the distribution of CCS shows a shell-like structure while that of NH_3 is concentrated at the center of the core. Abundances of carbon-chain molecules are higher in L1521E than the other dark cloud cores, and especially those of sulfur-bearing molecules C_nS are comparable to the cyanopolyyne peak of TMC-1. Our results suggest that L1521E would be in a very early stage of physical and chemical evolution.Comment: 10 pages, 3 EPS figures, uses aaspp4.sty and epsf.sty, AAS LaTeX macros v4.0, The Astrophysical Journal, in pres

Analytical three-dimensional bright solitons and soliton-pairs in Bose-Einstein condensates with time-space modulation

We provide analytical three-dimensional bright multi-soliton solutions to the (3+1)-dimensional Gross-Pitaevskii (GP) equation with time and space-dependent potential, time-dependent nonlinearity, and gain/loss. The zigzag propagation trace and the breathing behavior of solitons are observed. Different shapes of bright solitons and fascinating interactions between two solitons can be achieved with different parameters. The obtained results may raise the possibility of relative experiments and potential applications.Comment: 5 pages, 4 figure

Hypothesis of two-dimensional stripe arrangement and its implications for the superconductivity in high-Tc cuprates

The hypothesis that holes doped into high-Tc cuprate superconductors organize themselves in two-dimensional (2D) array of diagonal stripes is discussed, and, on the basis of this hypothesis, a new microscopic model of superconductivity is proposed and solved. The model describes two kinds of hole states localized either inside the stripes or in the antiferromagnetic domains between the stripes. The characteristic energy difference between these two kinds of states is identified with the pseudogap. The superconducting (SC) order parameter predicted by the model has two components, whose phases exhibit a complex dependence on the the center-of-mass coordinate. The model predictions for the tunneling characteristics and for the dependence of the critical temperature on the superfluid density show good quantitative agreement with a number of experiments. The model, in particular, predicts that the SC peaks in the tunneling spectra are asymmetric, only when the ratio of the SC gap to the critical temperature is greater than 4. It is also proposed that, at least in some high-Tc cuprates, there exist two different superconducting states corresponding to the same doping concentration and the same critical temperature. Finally, the checkerboard pattern in the local density of states observed by scanning tunneling microscopy in Bi-2212 is interpreted as coming from the states localized around the centers of stripe elements forming the 2D superstructure.Comment: Text close to the published version. This version is 10 per cent shorter than the previous one. All revisions are mino

Dynamical Reduction of Discrete Systems Based on the Renormalization Group Method

The renormalization group (RG) method is extended for global asymptotic analysis of discrete systems. We show that the RG equation in the discretized form leads to difference equations corresponding to the Stuart-Landau or Ginzburg-Landau equations. We propose a discretization scheme which leads to a faithful discretization of the reduced dynamics of the original differential equations.Comment: LaTEX. 12pages. 1 figure include

Complex Analysis of a Piece of Toda Lattice

We study a small piece of two dimensional Toda lattice as a complex dynamical system. In particular the Julia set, which appears when the piece is deformed, is shown analytically how it disappears as the system approaches to the integrable limit.Comment: 17 pages, LaTe

On a discrete Davey-Stewartson system

We propose a differential difference equation in ${\mathcal R}^1\times {\mathcal Z}^2$ and study it by Hirota's bilinear method. This equation has a singular continuum limit into a system which admits the reduction to the Davey-Stewartson equation. The solutions of this discrete DS system are characterized by Casorati and Grammian determinants. Based on the bilinear form of this discrete DS system, we construct the bilinear B\"{a}cklund transformation which enables us to obtain its Lax pair.Comment: 12 pages, 2 figure

Neutron Scattering Study of Temperature-Concentration Phase Diagram of (Cu1-xMgx)GeO3

In doped CuGeO3 systems, such as (Cu1-xZnx)GeO3 and Cu(Ge1-xSix)O3, the spin-Peierls (SP) ordering (T<Tsp) coexists with the antiferromagnetic (AF) phase (T<TN<Tsp). Tsp decreases while TN increases with increasing x in low doping region. For higher x, however, the SP state disappears and only the AF state remains. These features are common for all the doped CuGeO3 systems so far studied, indicating the existence of universal T-x phase diagram. Recently, Masuda et al. carried out comprehensive magnetic susceptibility (chi) measurements of (Cu1-xMgx)GeO3, in which doping concentration can be controlled significantly better than the Zn doped systems. They found that TN suddenly jumps from 3.43 to 3.98K at the critical concentration xc sim 0.023 and that a drop in chi corresponding to the SP ordering also disappears at x>xc. They thus concluded that there is a compositional phase boundary between two distinct magnetic phases. To clarify the nature of two phases, we performed neutron-scattering measurements on (Cu1-xMgx)GeO3 single crystals with various x. Analysis of the data at fixed temperature points as a function of doping concentration has revealed sudden changes of order parameters at the critical concentration xc=0.027 +- 0.001. At finite temperatures below TN, the drastic increase of the AF moment takes place at xc. The spin-Peierls order parameter delta associated with lattice dimerization shows a precipitous decrease at all temperature below Tsp. However, it goes to zero above xc only at the low temperature limit.Comment: 9 pages, 9 figure