Entangled coherent states: teleportation and decoherence

When a superposition $(|\alpha>-|-\alpha>)$ of two coherent states with opposite phase falls upon a 50-50 beamsplitter, the resulting state is entangled. Remarkably, the amount of entanglement is exactly 1 ebit, irrespective of $\alpha$, as was recently discovered by O. Hirota and M. Sasaki. Here we discuss decoherence properties of such states and give a simple protocol that teleports one qubit encoded in Schr\"odinger cat statesComment: 11 pages LaTeX, 3 eps figures. Submitted to Phys. Rev.

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

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.

Spin Dynamics of a Canted Antiferromagnet in a Magnetic Field

The spin dynamics of a canted antiferromagnet with a quadratic spin-wave dispersion near \vq =0 is shown to possess a unique signature. When the anisotropy gap is negligible, the spin-wave stiffness \dsw (\vq, B) = (\omega_{\vq}-B)/q^2 depends on whether the limit of zero field or zero wavevector is taken first. Consequently, \dsw is a strong function of magnetic field at a fixed wavevector. Even in the presence of a sizeable anisotropy gap, the field dependence of both \dsw and the gap energy distinguishes a canted antiferromagnet from a phase-separated mixture containing both ferromagnetic and antiferromagnetic regions.Comment: 10 pages, 3 figure

Supersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach

A proper bilinear form is proposed for the N=1 supersymmetric modified Korteweg-de Vries equation. The bilinear B\"{a}cklund transformation of this system is constructed. As applications, some solutions are presented for it.Comment: 8 pages, LaTeX using packages amsmath and amssymb, some corrections mad

An integrable generalization of the Toda law to the square lattice

We generalize the Toda lattice (or Toda chain) equation to the square lattice; i.e., we construct an integrable nonlinear equation, for a scalar field taking values on the square lattice and depending on a continuous (time) variable, characterized by an exponential law of interaction in both discrete directions of the square lattice. We construct the Darboux-Backlund transformations for such lattice, and the corresponding formulas describing their superposition. We finally use these Darboux-Backlund transformations to generate examples of explicit solutions of exponential and rational type. The exponential solutions describe the evolution of one and two smooth two-dimensional shock waves on the square lattice.Comment: 14 pages, 4 figures, to appear in Phys. Rev. E http://pre.aps.org

Multiple addition theorem for discrete and continuous nonlinear problems

The addition relation for the Riemann theta functions and for its limits, which lead to the appearance of exponential functions in soliton type equations is discussed. The presented form of addition property resolves itself to the factorization of N-tuple product of the shifted functions and it seems to be useful for analysis of soliton type continuous and discrete processes in the N+1 space-time. A close relation with the natural generalization of bi- and tri-linear operators into multiple linear operators concludes the paper.Comment: 9 page

A survey of Hirota's difference equations

A review of selected topics in Hirota's bilinear difference equation (HBDE) is given. This famous 3-dimensional difference equation is known to provide a canonical integrable discretization for most important types of soliton equations. Similarly to the continuous theory, HBDE is a member of an infinite hierarchy. The central point of our exposition is a discrete version of the zero curvature condition explicitly written in the form of discrete Zakharov-Shabat equations for M-operators realized as difference or pseudo-difference operators. A unified approach to various types of M-operators and zero curvature representations is suggested. Different reductions of HBDE to 2-dimensional equations are considered. Among them discrete counterparts of the KdV, sine-Gordon, Toda chain, relativistic Toda chain and other typical examples are discussed in detail.Comment: LaTeX, 43 pages, LaTeX figures (with emlines2.sty