New Boundary Bound States in an Open Quantum Spin Chain

New boundary bound states (BBS) are found of an integrable model with the magnetic impurities located at the edges of an open Heisenberg spin chain. These bound states carry the real energy and are formed by three or five imaginary modes of the rapidities. These imaginary modes of the rapidities give the non-zero antisymmetric wave functions and the moments of the centers of the bound states are zero. It means that these bound states are arisen by the magnetic impurities and localized at the edges of the correlated system. The Kondo screening occurs for the antiferromagnetic spin chain with the ferromagnetic impurities-electrons exchange interaction.Comment: 4 pages, Revte

Asymptotic behavior of the nonlinear Schr\"{o}dinger equation on exterior domain

{\bf Abstract} \,\, We consider the following nonlinear Schr\"{o}dinger equation on exterior domain. \begin{equation} \begin{cases} iu_t+\Delta_g u + ia(x)u - |u|^{p-1}u = 0 \qquad (x,t) \in \Omega\times (0,+\infty), \qquad (1)\cr u\big|_\Gamma = 0\qquad t \in (0,+\infty), \cr u(x,0) = u_0(x)\qquad x \in \Omega, \end{cases} \end{equation} where $1<p<\frac{n+2}{n-2}$, $\Omega\subset\mathbb{R}^n$ ($n\ge3$) is an exterior domain and $(\mathbb{R}^n,g)$ is a complete Riemannian manifold. We establish Morawetz estimates for the system (1) without dissipation ($a(x)\equiv 0$ in (1)) and meanwhile prove exponential stability of the system (1) with a dissipation effective on a neighborhood of the infinity. It is worth mentioning that our results are different from the existing studies. First, Morawetz estimates for the system (1) are directly derived from the metric $g$ and are independent on the assumption of an (asymptotically) Euclidean metric. In addition, we not only prove exponential stability of the system (1) with non-uniform energy decay rate, which is dependent on the initial data, but also prove exponential stability of the system (1) with uniform energy decay rate. The main methods are the development of Morawetz multipliers in non (asymptotically) Euclidean spaces and compactness-uniqueness arguments.Comment: 25 page

Weyl Pair, Current Algebra and Shift Operator

The Abelian current algebra on the lattice is given from a series of the independent Weyl pairs and the shift operator is constructed by this algebra. So the realization of the operators of the braid group is obtained. For $|q|\neq 1$ the shift operator is the product of the theta functions of the generators $w_n$ of the current algebra. For $|q|=1$ it can be expressed by the quantum dilogarithm of $w_n$.Comment: 8 pages, latex file, AS-ITP-94-5

Baxter-Bazhanov Model, Frenkel-Moore Equation and the Braid Group

In this paper the three-dimensional vertex model is given, which is the duality of the three-dimensional Baxter-Bazhanov (BB) model. The braid group corresponding to Frenkel-Moore equation is constructed and the transformations $R, I$ are found. These maps act on the group and denote the rotations of the braids through the angles $\pi$ about some special axes. The weight function of another three-dimensional vertex model related the 3D lattice integrable model proposed by Boos, Mangazeev, Sergeev and Stroganov is presented also, which can be interpreted as the deformation of the vertex model corresponding to the BB model.Comment: 14 pages, latex, 5 pasted figures (Page 13, 14

Topological quantum states of matter in iron-based superconductors: From concepts to material realization

We review recent progress in the explorations of topological quantum states of matter in iron-based superconductors. In particular, we focus on the nontrivial topology existing in the band structures and superconducting states of iron's 3d orbitals. The basic concepts, models, materials and experimental results are reviewed. The natural integration between topology and high-temperature superconductivity in iron-based superconductors provides great opportunities to study topological superconductivity and Majorana modes at high temperature.Comment: 13 pages, 4 figures. A review article for National Science Revie

A Riemann-Hilbert Approach to the Complex Sharma-Tasso-Olver Equation on the Half Line

In this paper, we use the Fokas method to analyze the complex Sharma-Tasso-Olver(cSTO) equation on the half line. We show that it can be represented in terms of the solution of a matrix RHP formulated in the plane of the complex spectral parameter {\lambda}.Comment: arXiv admin note: text overlap with arXiv:1109.4935, arXiv:1205.1559, arXiv:0808.1534 by other author

Quantum measurement of an electron in disordered potential: delocalization versus measurement voltages

Quantum point contact (QPC), one of the typical mesoscopic transport devices, has been suggested to be an efficient detector for quantum measurement. In the context of two-state charge qubit, our previous studies showed that the QPC's measurement back-action cannot be described by the conventional Lindblad quantum master equation. In this work, we study the measurement problem of a multi-state system, say, an electron in disordered potential, subject to the quantum measurement of the mesoscopic detector QPC. The effect of measurement back-action and the detector's readout current are analyzed, where particular attention is focused on some new features and the underlying physics associated with the measurement-induced delocalization versus the measurement voltages.Comment: 5pages, 4figure

Solutions of n-simplex Equation from Solutions of Braid Group Representation

It is shown that a kind of solutions of n-simplex equation can be obtained from representations of braid group. The symmetries in its solution space are also discussed.Comment: 8 pages, latex. The figures can be get from the author

Remarks on the Star-Triangle Relation in the Baxter-Bazhanov Model

In this letter we show that the restricted star-triangle relation introduced by Bazhanov and Baxter can be obtained either from the star-triangle relation of chiral Potts model or from the star-square relation which is proposed by Kashaev $et ~al$ and give a response of the guess which is suggested by Bazhanov and Baxter in Ref. \cite{b2}.Comment: 6 pages, latex file, AS-ITP-94-3

Cyclic Quantum Dilogarithm and Shift Operator

{}From the cyclic quantum dilogarithm the shift operator is constructed with $q$ is a root of unit and the representation is given for the current algebra introduced by Faddeev $et ~al$. It is shown that the theta-function is factorizable also in this case by using the star-square equation of the Baxter-Bazhanov model.Comment: 9 pages, latex, no figure