M\"obius Symmetry of Discrete Time Soliton Equations

We have proposed, in our previous papers, a method to characterize integrable discrete soliton equations. In this paper we generalize the method further and obtain a $q$-difference Toda equation, from which we can derive various $q$-difference soliton equations by reductions.Comment: 21 pages, 4 figure, epsfig.st

Two-dimensional soliton cellular automaton of deautonomized Toda-type

A deautonomized version of the two-dimensional Toda lattice equation is presented. Its ultra-discrete analogue and soliton solutions are also discussed.Comment: 11 pages, LaTeX fil

Electric Control of Spin Helicity in a Magnetic Ferroelectric

Magnetic ferroelectrics or multiferroics, which are currently extensively explored, may provide a good arena to realize a novel magnetoelectric function. Here we demonstrate the genuine electric control of the spiral magnetic structure in one of such magnetic ferroelectrics, TbMnO3. A spin-polarized neutron scattering experiment clearly shows that the spin helicity, clockwise or counter-clockwise, is controlled by the direction of spontaneous polarization and hence by the polarity of the small cooling electric field.Comment: 4 pages, 3 figure

Third-order integrable difference equations generated by a pair of second-order equations

We show that the third-order difference equations proposed by Hirota, Kimura and Yahagi are generated by a pair of second-order difference equations. In some cases, the pair of the second-order equations are equivalent to the Quispel-Robert-Thomson(QRT) system, but in the other cases, they are irrelevant to the QRT system. We also discuss an ultradiscretization of the equations.Comment: 15 pages, 3 figures; Accepted for Publication in J. Phys.

Zn and Ni doping effects on the low-energy spin excitations in La1.85_{1.85}Sr0.15_{0.15}CuO4_{4}

Impurity effects of Zn and Ni on the low-energy spin excitations were systematically studied in optimally doped La1.85Sr0.15Cu1-yAyO4 (A=Zn, Ni) by neutron scattering. Impurity-free La1.85Sr0.15CuO4 shows a spin gap of 4meV below Tc in the antiferromagnetic(AF) incommensurate spin excitation. In Zn:y=0.004, the spin excitation shows a spin gap of 3meV below Tc. In Zn:y=0.008 and Zn:y=0.011, however, the magnetic signals at 3meV decrease below Tc and increase again at lower temperature, indicating an in-gap state. In Zn:y=0.017, the low-energy spin state remains unchanged with decreasing temperature, and elastic magnetic peaks appear below 20K then exponentially increase. As for Ni:y=0.009 and Ni:y=0.018, the low-energy excitations below 3meV and 2meV disappear below Tc. The temperature dependence at 3meV, however, shows no upturn in constrast with Zn:y=0.008 and Zn:y=0.011, indicating the absence of in-gap state. In Ni:y=0.029, the magnetic signals were observed also at 0meV. Thus the spin gap closes with increasing Ni. Furthermore, as omega increases, the magnetic peak width broadens and the peak position, i.e. incommensurability, shifts toward the magnetic zone center (pi pi). We interpret the impurity effects as follows: Zn locally makes a non-superconducting island exhibiting the in-gap state in the superconducting sea with the spin gap. Zn reduces the superconducting volume fraction, thus suppressing Tc. On the other hand, Ni primarily affects the superconducting sea, and the spin excitations become more dispersive and broaden with increasing energy, which is recognized as a consequence of the reduction of energy scale of spin excitations. We believe that the reduction of energy scale is relevant to the suppression of Tc.Comment: 13pages, 14figures; submitted to Phys. Rev.

Zero curvature representation for classical lattice sine-Gordon equation via quantum R-matrix

Local M-operators for the classical sine-Gordon model in discrete space-time are constructed by convolution of the quantum trigonometric 4$\times$4 R-matrix with certain vectors in its "quantum" space. Components of the vectors are identified with $\tau$-functions of the model. This construction generalizes the known representation of M-operators in continuous time models in terms of Lax operators and classical $r$-matrix.Comment: 10 pages, LaTeX (misprints are corrected