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- Construction of the bethe state for the E-tau,E-eta(so(3)) elliptic quantum groupPublication . Manojlovic, Nenad; Nagy, Zoltan
Expand Elliptic quantum groups can be associated to solutions of the star-triangle relation of statistical mechanics. In this paper, we consider the particular case of the E-tau,E-eta(so(3)) elliptic quantum group. In the context of algebraic Bethe ansatz, we construct the corresponding Bethe creation operator for the transfer matrix defined in an arbitrary representation of E-tau,E-eta(so(3)).Expand - Algebraic Bethe ansatz for the Sl(2) Gaudin model with boundaryPublication . Cirilo Antonio, N.; Manojlović, Nenad; Ragoucy, E.; Salom, I.
Expand Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaudin Hamiltonians with boundary terms. Our derivation is based on the quasi-classical expansion of the linear combination of the transfer matrix of the XXX Heisenberg spin chain and the central element, the so-called Sklyanin determinant. The corresponding Gaudin Hamiltonians with boundary terms are obtained as the residues of the generating function. By defining the appropriate Bethe vectors which yield strikingly simple off shell action of the generating function, we fully implement the algebraic Bethe ansatz, obtaining the spectrum of the generating function and the corresponding Bethe equations. (C) 2015 Published by Elsevier B.V.Expand - Standing wave solutions in Born-Infeld theoryPublication . Manojlovic, Nenad; Perlick, Volker; Potting, Robertus
Expand We study standing-wave solutions of Born-Infeld electrodynamics, with nonzero electromagnetic field in a region between two parallel conducting plates. We consider the simplest case which occurs when the vector potential describing the electromagnetic field has only one nonzero component depending on time and on the coordinate perpendicular to the plates. the problem then reduces to solving the scalar Born-Infeld equation, a nonlinear partial differential equation in 1+1 dimensions. We apply two alternative methods to obtain standing-wave solutions to the Born-Infeld equation: an iterative method, and a "minimal surface" method. We also study standing wave solutions in a uniform constant magnetic field background. the results obtained in this work provide a theoretical background for experimental tests of Born-Infeld theory. (C) 2020 Elsevier Inc. All rights reserved.Expand - Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson modelsPublication . Skrypnyk, T.; Manojlović, Nenad
Expand In the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric gl(2) circle times gl(2)-valued Cartan-non-invariant classical r-matrices with spectral parameters. We consider the two families of these r-matrices, namely, the two non-standard rational r-matrices twisted with the help of second order automorphisms and realize the algebraic Bethe ansatz method for them. We study physically important examples of the Gaudin-type and BCS-type systems associated with these r-matrices and obtain explicitly the Bethe vectors and the spectrum for the corresponding quantum hamiltonians in terms of solutions of Bethe equations. (C) 2021 The Author(s). Published by Elsevier B.V.Expand - Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin modelPublication . Antonio, N. Cirilo; Manojlović, Nenad; Salom, I.
Expand We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression for the off shell action of the transfer matrix, deriving the spectrum and the relevant Bethe equations. We explore further these results by obtaining the off shell action of the generating function of the Gaudin Hamiltonians on the corresponding Bethe vectors through the so-called quasi-classical limit. Moreover, this action is as simple as it could possibly be, yielding the spectrum and the Bethe equations of the Gaudin model. (C) 2014 The Authors. Published by Elsevier B.V.Expand - Generalized sℓ(2) Gaudin algebra and corresponding Knizhnik–Zamolodchikov equationPublication . Salom, I.; Manojlović, Nenad; Cirilo António, N.
Expand The Gaudin model has been revisited many times, yet some important issues remained open so far. With this paper we aim to properly address its certain aspects, while clarifying, or at least giving a solid ground to some other. Our main contribution is establishing the relation between the off-shell Bethe vectors with the solutions of the corresponding Knizhnik-Zamolodchikov equations for the non-periodic sl(2) Gaudin model, as well as deriving the norm of the eigenvectors of the Gaudin Hamiltonians. Additionally, we provide a closed form expression also for the scalar products of the off-shell Bethe vectors. Finally, we provide explicit closed form of the off-shell Bethe vectors, together with a proof of implementation of the algebraic Bethe ansatz in full generality. (C) 2019 The Authors.Expand - Bethe states and Knizhnik-Zamolodchikov equations of the trigonometric Gaudin model with triangular boundaryPublication . Salom, I.; Manojlović, Nenad
Expand We present a comprehensive treatment of the non-periodic trigonometric s (2) Gaudin model with tri angular boundary, with an emphasis on specific freedom found in the local realization of the generators, as well as in the creation operators used in the algebraic Bethe ansatz. First, we give Bethe vectors of the non-periodic trigonometric s (2) Gaudin model both through a recurrence relation and in a closed form. Next, the off-shell action of the generating function of the trigonometric Gaudin Hamiltonians with gen eral boundary terms on an arbitrary Bethe vector is shown, together with the corresponding proof based on mathematical induction. The action of the Gaudin Hamiltonians is given explicitly. Furthermore, by careful choice of the arbitrary functions appearing in our more general formulation, we additionally obtain: i) the solutions to the Knizhnik-Zamolodchikov equations (each corresponding to one of the Bethe states); ii) compact formulas for the on-shell norms of Bethe states; and iii) closed-form expressions for the off-shell scalar products of Bethe states.Expand - Rational so(3) Gaudin model with general boundary termsPublication . Manojlović, Nenad; Salom, I.
Expand We study the so(3) Gaudin model with general boundary K-matrix in the framework of the algebraic Bethe ansatz. The off-shell action of the generating function of the so(3) Gaudin Hamiltonians is determined. The proof based on the mathematical induction is presented on the algebraic level without any restriction whatsoever on the boundary parameters. The so(3) Gaudin Hamiltonians with general boundary terms are given explicitly as well as their off-shell action on the Bethe states. The correspondence between the Bethe states and the solutions to the generalized so(3) Knizhnik-Zamolodchikov equations is established. In this context, the on-shell norm of the Bethe states is determined as well as their off-shell scalar product.Expand - Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundaryPublication . Manojlovic, Nenad; Salom, Igor
Expand In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model.Expand - G(2)-Calogero-Moser Lax operators from reductionPublication . Fring, Andreas; Manojlovic, Nenad
Expand We construct a Lax operator for the G(2)-Calogero-Moser model by means of a double reduction procedure. In the first reduction step we reduce the A(6)-model to a B-3-model with the help of an embedding of the B-3-root system into the A(6)-root system together with the specification of certain coupling constants. The G(2)-Lax operator is obtained thereafter by means of an additional reduction by exploiting the embedding of the G(2)-system into the B-3-system. The degree of algebraically independent and non-vanishing charges is found to be equal to the degrees of the corresponding Lie algebra.Expand