Papers by Nenad Manojlović
Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek Iists this... more Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek Iists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>.
Progress in Mathematics, 2005
Bibliographic information published b; Hie Deutsche Ribliothck Die Deutsche Bihliothek lists this... more Bibliographic information published b; Hie Deutsche Ribliothck Die Deutsche Bihliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at <http://dnb.ddb.de>. ISBN 3-7643-7215-X Birkhauser Verlag, Basel-Boston-Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use whatsoever, permission from the copyright owner must be obtained.
Journal of Mathematical Sciences, 2008
Symmetry Integr Geom, 2007
Nuclear Physics B, 2015
Following Sklyanin's proposal in the periodic case, we derive the generating function of the Gaud... more 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 quasiclassical 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.
Factorization and Integrable Systems, 2003
Mathematical Methods in the Applied Sciences, 2001
ABSTRACT The Ruijgrok–Wu model of the kinetic theory of rarefied gases is investigated both in th... more ABSTRACT The Ruijgrok–Wu model of the kinetic theory of rarefied gases is investigated both in the fluid-dynamic and hydro-dynamic scalings. It is shown that the first limit equation is a first order quasilinear conservation law, whereas the limit equation in the diffusive scaling is the viscous Burgers equation. The main difficulties came from initial layers that we handle here. Copyright © 2001 John Wiley &amp; Sons, Ltd.
The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, w... more The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.
Nuclear Physics B, 2018
The Gaudin model has been revisited many times, yet some important issues remained open so far. W... more 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 s (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.
Theoretical and Mathematical Physics, 2016
We construct quantum integrable systems associated with the Lie algebra gl(n) and non-skew-symmet... more We construct quantum integrable systems associated with the Lie algebra gl(n) and non-skew-symmetric "shifted and twisted" rational r-matrices. The obtained models include Gaudin-type models with and without an external magnetic field, n-level (n−1)-mode Jaynes-Cummings-Dicke-type models in the Λconfiguration, a vector generalization of Bose-Hubbard dimers, etc. We diagonalize quantum Hamiltonians of the constructed integrable models using a nested Bethe ansatz.
Asymptotic behaviour of cylindrical waves interacting with
Symmetry, Integrability and Geometry: Methods and Applications, 2007
Elliptic quantum groups can be associated to solutions of the star-triangle relation of statistic... more 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 $E_{tau,eta)(so_3)$ 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 $E_{tau,eta)(so_3)$.
We examine the reduced phase space of the Bianchi VII0 cosmological model, including the moduli s... more We examine the reduced phase space of the Bianchi VII0 cosmological model, including the moduli sector. We show that the dynamics of the relevant sector of local degrees of freedom is given by a Painlevé III equation. We then obtain a zerocurvature representation of this Painlevé III equation by applying the Belinskii-Zakharov method to the Bianchi VII0 model.
Asymptotic behaviour of cylindrical waves interacting with
Reviews in Mathematical Physics
Journal of Mathematical Physics, 2011
The Gaudin model based on the sl2-invariant r-matrix with an extra Jordanian term depending on th... more The Gaudin model based on the sl2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a recurrence relation. The commutation relations between the generating function t(λ) of the integrals of motion and the creation operators are calculated and therefore the algebraic Bethe Ansatz is fully implemented. The energy spectrum as well as the corresponding Bethe equations of the system coincide with the ones of the sl2-invariant Gaudin model. As opposed to the sl2-invariant case, the operator t(λ) and the Gaudin Hamiltonians are not hermitian. Finally, the inner products and norms of the Bethe states are studied.
Journal of Mathematical Physics, 2011
The Gaudin model based on the sl(2)-invariant r-matrix with an extra Jordanian term depending on ... more The Gaudin model based on the sl(2)-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a recurrence relation. The commutation relations between the generating function t(λ) of the integrals of motion and the creation operators are calculated and therefore the algebraic Bethe Ansatz is fully implemented. The energy spectrum, as well as the corresponding Bethe equations of the system, coincide with the ones of the sl2-invariant Gaudin model. As opposed to the sl2-invariant case, the operator t(λ) and the Gaudin Hamiltonians are not Hermitian. Finally, the inner products and norms of the Bethe states are studied.
Proceedings of a Conference held at the Isaac Newton Institute, Cambridge, June 1994, 1995
Journal of Mathematical Physics, 2000
We show that α < 0, β > 0, γ = δ = 0 Painlevé III equation arises as a zerocurvature condition in... more We show that α < 0, β > 0, γ = δ = 0 Painlevé III equation arises as a zerocurvature condition in the Belinskii-Zakharov inverse scattering formulation for Bianchi cosmological models. For special values of the parameters this Painlevé III equation becomes the dynamical equation for Bianchi I, II, VI 0 and VII 0 models.
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Papers by Nenad Manojlović