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- Construction of the bethe state for the E-tau,E-eta(so(3)) elliptic quantum groupPublication . Manojlovic, Nenad; Nagy, ZoltanElliptic 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)).
- Standing wave solutions in Born-Infeld theoryPublication . Manojlovic, Nenad; Perlick, Volker; Potting, RobertusWe 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.
- Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundaryPublication . Manojlovic, Nenad; Salom, IgorIn 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.
- G(2)-Calogero-Moser Lax operators from reductionPublication . Fring, Andreas; Manojlovic, NenadWe 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.