The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin, and the Z2-graded 19-vertex models with sl(2|1) and osp(1|2) invariances. In each case the eigenspectrum is determined by application of the coordinate Bethe Ansatz.PACS: 05.20.-y, 05.50.+q, 04.20.Jb.
The semi-classical limit of the algebraic Bethe Ansatz method is used to solve the theory of Gaudin models. Via the off-shell method we find the spectra and eigenvectors of the N − 1 independent Gaudin Hamiltonians with symmetry osp(2|1). We also show how the off-shell Gaudin equation solves the trigonometric Knizhnik-Zamolodchikov equation.
This work is concerned with the formulation of the boundary quantum inverse scattering method for the xxz Gaudin magnet coupled to boundary impurities with arbitrary exchange constants. The Gaudin magnet is diagonalized by taking a quasi-classical limit of the inhomogeneous lattice. Using the method proposed by Babujian, the integral representation for the solution of the Knizhnik-Zamolodchikov equation is explictly constructed and its rational limit discussed.Integrable quantum field theories with boundaries have been subject of intense study during the past decades. The great interest in such theories stems from the large number of potential applications in different areas in physics, including open strings, boundary conformal field theory, dissipative quantum phenomena and impurity problems.The Gaudin magnet has its origins in [1] as a quantum integrable model describing N spin-1 2 particles with long-range interactions. The Gaudin type models have direct applications in condensed matter physics. They also have been used as a testing ground for ideas such as the functional Bethe ansatz (BA) and general procedure of separation of variables [2,3,4]. The model proposed by Gaudin was later generalized by several authors [5, 6, 7]. The spin-s XXY Gaudin model was solved in [8] by means of the off-shell algebraic BA.The XYZ Gaudin model was constructed and solved in [3] and [9] by means of the algebraic BA method. The boundary XXY spin-1 2 Gaudin magnet was investigated by Hikami [10] and the Gaudin models based on the face-type elliptic quantum groups and boundary elliptic quantum group, as well as, the boundary XYZ Gaudin models were studied in [11] by means of the boundary algebraic BA method.In [12] the XXZ Gaudin model was solved with generic integrable boundaries specified by generic nondiagonal K-matrices.The Knizhnik-Zamolodchikov (KZ) equations were first proposed as a set of differential equations satisfied by correlation functions of the Wess-Zumino-Witten models [13]. The relations between the Gaudin magnets and the KZ equations has been studied in many papers [8,14,15,16,17,18]. In [10], Hikami gave an integral representation for the solutions of the KZ equations by using the results of the boundary Gaudin model.In addition, the quantum impurity problem, which has been extensively investigated with renormalizing group techniques [19] and conformal field theory [20], is also very interesting in itself. Andrei and Johannesson [21] first considered an impurity spin-s embedded in an integrable spin-1 2 XXX chain with periodic boundary conditions. Subsequently, Schlottmann et al [22] generalized it to the arbitrary spin chain. The standard approach to dealing with the impurity integrable problem is also the algebraic BA
Neste artigo, investigaremos a criação de realismo visual através da simulação visual de fenômenos naturais complexos em ambientes virtuais 3D. Para isto, serão utilizados os chamadossistemas de partículas. Discutiremos como utilizá-los no ensino, com ênfase em ciências exatas e tecnológicas, visando aumentar o interesse do aluno e facilitar o aprendizado do conteúdo ensinado.Será abordada também a conveniência do uso de técnicas de modelagem tradicionais em 3D para determinadas situações.
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