Antonio Lima Santos

• Abstract

  Temperley-Lieb spin chains are a class of one-dimensional quantum mechanical models that are integrate. An exact algebraic Bethe Ansatz solution of these models will be proposed, and related problems will be investigated. (AU)

  Temperley-Lieb spin chains, AP.R SPRINT

• Abstract

  In this project we intend to contribute to the development of the algebraic Bethe ansatz as a technique to solve vertex models with open boundary conditions. Recent breakthroughs will be taken into account in order to investigate problems such as the calculation of scalar products and correlation functions for models with non-diagonal reflection matrices. (AU)

  Bethe ansatz for non-diagonal boundaries, AV.EXT

• Abstract

  In the last decade new observational and theoretical results have given a new impulse on the investigation of structural questions and phenomenological applications of general relativity. On one hand, cosmology is in a period where new data suggest new and challenging visions of the universe. In this context, new approaches are necessary to explain what is observed and also what is not di…

  Gravitation and cosmology: structural questions and applications, AP.TEM

(Only some records are available in English at this moment)

• Abstract

  We shall analyze many aspects concerning the integrability for systems with open boundaries conditions. Our main focus will be the study of vertex models with non-diagonal reflection matrices by means of Bethe ansatz techniques, including their algebraic and analytical versions. Possible applications in the AdS/CFT correspondence will be also considered.

  Open boundary integrability: theory and applications, BP.PD

• Abstract

  The aim of this project is to study the reflection equationfor R-matrices, solutions of the Yang-Baxter equation,that violate the symmetries usually assumed in this context.In particular, we shall analyze the reflection equation for three-statevertex models violating the charge symmetry,for models with R-matrix enjoying additiveand non-additive spectral parameters andfor nineteen-vertex m…

  Integrable Boundaries in Statistical Mechanics, BP.DR

• Abstract

  We will study integrals in matrix spaces, in particular the ensemble of hermitian matrices whose elements are random variables with Gaussian distribution. This ensemble, invariant under unitary transformations, is known as the Gaussian Unitary Ensemble. We will see, introductorily, some of the many applications that matrix integrals have in mathematics and physics. For examples, integrals…

  Introduction to random matrices, BP.IC

(Only some records are available in English at this moment)

• Abstract

  By means of algebraic Bethe ansatz techniques, we will investigate the spectral problem of vertex models with non-periodic boundary conditions. In particular, using similarity transformations and fusion techniques, we expect to construct Bethevectors for the SU(2)-invariant Heisenberg spin-s chain with general integrable boundary conditions. (AU)

  Exact solution of vertex models with open boundaries, BE.EP.PD