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Autor: Vincent Pasquier, O. Babelon, Karol K. Kozlowski

Publikováno v: Letters in Mathematical Physics. 109:225-241

We show that a natural discretisation of Virasoro algebra yields a quantum integrable model which is the Toda chain in the second Hamiltonian structure.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::c6a905f624689caaa9d6f0ac15878d5c
https://doi.org/10.1007/s11005-018-1111-y

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Baxter operator and Baxter equation for $q$-Toda and Toda$_2$ chains

Autor: Vincent Pasquier, Karol K. Kozlowski, O. Babelon

Publikováno v: Reviews in Mathematical Physics
Reviews in Mathematical Physics, 2018, 30 (06), pp.1840003. ⟨10.1142/S0129055X18400032⟩
Rev.Math.Phys.
Rev.Math.Phys., 2018, 30 (06), pp.1840003. ⟨10.1142/S0129055X18400032⟩

We construct the Baxter operator $\boldsymbol{ \texttt{Q} }(\lambda)$ for the $q$-Toda chain and the Toda$_2$ chain (the Toda chain in the second Hamiltonian structure). Our construction builds on the relation between the Baxter operator and B\"acklu

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a2823ad143e71c4cf6e2388ece840f9b
https://hal.science/hal-01797131

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Solution of Baxter equation for the $q$-Toda and Toda$_2$ chains by NLIE

Autor: O. Babelon, Vincent Pasquier, Karol K. Kozlowski

Publikováno v: SciPost Phys.
SciPost Phys., 2018, 5 (4), pp.035. ⟨10.21468/SciPostPhys.5.4.035⟩
SciPost Physics
SciPost Physics, SciPost Foundation, 2018, 5 (4), pp.035. ⟨10.21468/SciPostPhys.5.4.035⟩
SciPost Physics, 2018, 5 (4), pp.035. ⟨10.21468/SciPostPhys.5.4.035⟩
SciPost Physics, Vol 5, Iss 4, p 035 (2018)

We construct a basis of solutions of the scalar $\boldsymbol{ \texttt{t} }- \boldsymbol{ \texttt{Q} }$ equation describing the spectrum of the $q$-Toda and Toda$_2$ chains by using auxiliary non-linear integral equations. Our construction allows us t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8e8b2dd1f7ff358bed683325d67e3f4d
https://hal.archives-ouvertes.fr/hal-01797130

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Classical Bethe Ansatz and normal forms in an integrable version of the Dicke model

Autor: O. Babelon, B. Douçot

Publikováno v: Physica D: Nonlinear Phenomena. 241:2095-2108

The Dicke–Jaynes–Cummings–Gaudin model describes a collection of n spins coupled to a harmonic oscillator. It is known to be integrable, so one can define a moment map which associates to each point in phase space the list of values of the n +

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::07ec4a9a501927614f6e686dae1d7e87
https://doi.org/10.1016/j.physd.2012.03.009

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Form factors, KdV and deformed hyperelliptic curves

Autor: F.A. Smirnov, Denis Bernard, O. Babelon

Publikováno v: Nuclear Physics B-Proceedings Supplements
Nuclear Physics B-Proceedings Supplements, Elsevier, 1997, 58, pp.21-33. ⟨10.1016/S0920-5632(97)00410-6⟩
Nuclear Physics B-Proceedings Supplements, 1997, 58, pp.21-33. ⟨10.1016/S0920-5632(97)00410-6⟩

We review and summarize recent works on the relation between form factors in integrable quantum field theory and deformation of geometrical data associated to hyper-elliptic curves. This relation, which is based on a deformation of the Riemann biline

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f377fab22681a9b693a4d513f307db35
https://doi.org/10.1016/s0920-5632(97)00410-6

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Kowalevski's Analysis of the Swinging Atwood's Machine

Autor: O Babelon, M. Talon, M. Capdequi Peyranère

Publikováno v: Journal of Physics A: Mathematical and Theoretical
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2010, 43 (8), pp.085207. ⟨10.1088/1751-8113/43/8/085207⟩
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (8), pp.085207. ⟨10.1088/1751-8113/43/8/085207⟩

We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is a infinite number of mass ratios $M/m$ where such expansions exist with the maximal number of arbitrary constants. These expansions are of t

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ca8ce6f5c3a6e1e9d848ea3b305decf
https://hal.archives-ouvertes.fr/hal-00420854/file/atwood.pdf

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Separation of variables for the classical and quantum Neumann model

Autor: O. Babelon, M. Talon

Publikováno v: Nuclear Physics B. 379:321-339

The method of separation of variables is shown to apply to both the classical and quantum Neumann model. In the classical case this nicely yields the linearization of the flow on the Jacobian of the spectral curve. In the quantum case the Schr\"oding

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e7a419ac451da3a8f6f5b76de5e927ea
https://doi.org/10.1016/0550-3213(92)90599-7

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Integrability and conformal invariance

Autor: L. Bonora, O. Babelon

Publikováno v: Nuclear Physics B - Proceedings Supplements. 18:10-15

The conformal affine Liouville model is introduced and discussed. This model reduces to the ordinary Liouville model or to the Sinh-Gordon model under certain limiting conditions. The corresponding exchange algebra is discussed.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::439f92f2e8f9fc0720943a601ba5cb94
https://doi.org/10.1016/0920-5632(91)90117-w

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Exchange Algebra in the Conformal Affine sl 2 Toda Field Theory

Autor: O. Babelon, L. Bonora

Publikováno v: Differential Geometric Methods in Theoretical Physics ISBN: 9783540537632

We analyse the sl2 affine Toda field theory introduced elsewhere. In particular we study the chiral splitting of the theory and the relevant Drinfeld-Sokolov equations. We exhibit the chiral exchange algebra and the conformal properties of objects in

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::b84f22660bbfec57d0f0e961b3bc7e65
https://doi.org/10.1007/3-540-53763-5_56

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From integrable to conformal theory

Autor: O. Babelon

Publikováno v: Nuclear Physics B - Proceedings Supplements. 18:1-22

Working in the context of Toda field theory, we establish the relationship between their integrability properties and their conformal structure, thereby clarifying the role of the Yang-Baxter equation in conformal field theory.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::fc2cd97f80095f399e7c5233d5b4997e
https://doi.org/10.1016/0920-5632(90)90644-a

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