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Pascal Baseilhac

Bio: Pascal Baseilhac is an academic researcher from University of Orléans. The author has contributed to research in topics: Boundary value problem & Basis (universal algebra). The author has an hindex of 24, co-authored 77 publications receiving 1933 citations. Previous affiliations of Pascal Baseilhac include Centre de Recherches Mathématiques & University of Montpellier.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the transfer matrix of the XXZ open spin-½ chain with general integrable boundary conditions and generic anisotropy parameter (q is not a root of unity and |q| = 1) is diagonalized using the representation theory of the q-Onsager algebra.
Abstract: The transfer matrix of the XXZ open spin-½ chain with general integrable boundary conditions and generic anisotropy parameter (q is not a root of unity and |q| = 1) is diagonalized using the representation theory of the q-Onsager algebra. Similarly to the Ising and superintegrable chiral Potts models, the complete spectrum is expressed in terms of the roots of a characteristic polynomial of degree d = 2N. The complete family of eigenstates are derived in terms of rational functions defined on a discrete support which satisfy a system of coupled recurrence relations. In the special case of linear relations between left and right boundary parameters for which Bethe-type solutions are known to exist, our analysis provides an alternative derivation of the results of Nepomechie et al and Cao et al. In the latter case the complete family of eigenvalues and eigenstates splits into two sets, each associated with a characteristic polynomial of degree d < 2N. Numerical checks performed for small values of N support the analysis.

169 citations

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TL;DR: In this paper, a new family of quantum integrable models is proposed, which is generated by a dual pair of operators { A, A ∗ ∈ A subject to q-deformed Dolan-Grady relations.

124 citations

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TL;DR: In this paper, the half-infinite XXZ open spin chain with general integrable boundary conditions is considered within the recently developed Onsager approach, and it is shown that the transfer matrix is simply expressed in terms of the elements of a new type of current algebra.

120 citations

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TL;DR: In this article, the standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction.

112 citations

Journal ArticleDOI
TL;DR: In this paper, a new (in)finite dimensional algebra which is a fundamental dynamical symmetry of a large class of (continuum or lattice) quantum integrable models is introduced and studied in details.

108 citations


Cited by
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01 Aug 1993
TL;DR: One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References as discussed by the authors
Abstract: One-dimensional Bose-gas One-dimensional Heisenberg magnet Massive Thirring model Classical r-matrix Fundamentals of inverse scattering method Algebraic Bethe ansatz Quantum field theory integral models on a lattice Theory of scalar products Form factors Mean value of operator Q Assymptotics of correlation functions Temperature correlation functions Appendices References.

1,491 citations

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TL;DR: Chari and Pressley as mentioned in this paper have published a book called "Chari, Pressley, and Chari: A Conversation with Vyjayanthi Chari and Andrew Pressley".
Abstract: By Vyjayanthi Chari and Andrew Pressley: 651 pp., £22.95 (US$34.95), isbn 0 521 55884 0 (Cambridge University Press, 1994).

761 citations

01 Sep 1976
TL;DR: In this article, the authors present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations, which they solve exactly using a kind of perturbational approach.
Abstract: The main purpos e of this chapter is to present a direct and systematic way of finding exact solutions and Backlund transformations of a certain class of nonlinear evolution equations. The nonlinear evolution equations are transformed, by changing the dependent variable(s), into bilinear differential equations of the following special form $$ F\left( {\frac{\partial }{{\partial t}} - \frac{\partial }{{\partial {t^1}}},\frac{\partial }{{\partial x}} - \frac{\partial }{{\partial {x^1}}}} \right)f(t,x)f({t^1},{x^1}){|_{t = {t^1},x = {x^1}}} = 0 $$ , which we solve exactly using a kind of perturbational approach.

612 citations

Journal ArticleDOI
TL;DR: In this article, the authors consider the dynamics of anti-D3 branes inside the Klebanov-Strassler geometry, the deformed conifold with M units of RR 3-form flux around the S3, and find that for p << M the system relaxes to a nonsupersymmetric NS 5-brane ''giant graviton' configuration, which is classically stable, but quantum mechanically can tunnel to a nearby supersymmetric vacuum with M−p D3 brane.
Abstract: We consider the dynamics of p anti-D3 branes inside the Klebanov-Strassler geometry, the deformed conifold with M units of RR 3-form flux around the S3. We find that for p << M the system relaxes to a nonsupersymmetric NS 5-brane `giant graviton' configuration, which is classically stable, but quantum mechanically can tunnel to a nearby supersymmetric vacuum with M−p D3 branes. This decay mode is exponentially suppressed and proceeds via the nucleation of an NS 5-brane bubble wall. We propose a dual field theory interpretation of the decay as the transition between a nonsupersymmetric `baryonic' branch and a supersymmetric `mesonic' branch of the corresponding SU(2M−p) × SU(M−p) low energy gauge theory. The NS 5-brane tunneling process also provides a simple visualization of the geometric transition by which D3-branes can dissolve into 3-form flux.

522 citations

Journal ArticleDOI
Yu Nakayama1
TL;DR: In this paper, a review of the recent developments of the Liouville field theory and its matrix model dual is presented, which includes some original material such as the derivation of the conjectured dual action for the N = 2 LiOUville theory from other known dualities and the comparison of the cross-cap state with the c = 0 unoriented matrix model.
Abstract: We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. In part III, the Liouville theory on unoriented surfaces is reviewed. After introducing the crosscap state, we discuss the matrix model dual description and the tadpole cancellation condition. This review also includes some original material such as the derivation of the conjectured dual action for the N = 2 Liouville theory from other known dualities and the comparison of the Liouville crosscap state with the c = 0 unoriented matrix model. This is based on my master’s thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2004.

429 citations