A New Model in the Calogero–Ruijsenaars Family

Marshall, Ian

doi:10.1007/s00220-015-2388-7

Cited by 12 publications

(82 citation statements)

References 29 publications

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“…We point out that the reduced system, which contains 3 independent coupling constants besides the deformation parameter, can be recovered (at least on a dense submanifold) as a singular limit of the standard 5-coupling deformation due to van Diejen. Our findings complement and further develop those obtained recently by Marshall [86] on the hyperbolic case by reduction of the Heisenberg double of SU(n, n).…”

Section: A Poisson-lie Deformationsupporting

confidence: 90%

“…Marshall [86] obtained similar results for an analogous deformation of the hyperbolic BC n Sutherland Hamiltonian. His deformed Hamiltonian differs from (3.1) above in some important signs and in the relevant domain of the 'position variables'p.…”

Section: Suthmentioning

confidence: 62%

“…His deformed Hamiltonian differs from (3.1) above in some important signs and in the relevant domain of the 'position variables'p. Although in our impression the completeness of the reduced Hamiltonian flows was not treated in a satisfactory way in [86], the completeness proof that we shall present can be adapted to Marshall's case as well, as demonstrated in Section 3.4.…”

Section: Suthmentioning

confidence: 93%

“…Although this is essentially analytic continuation, it should be noted that the resulting systems are qualitatively different in their dynamical characteristics and global features. In addition, what we hope makes our work worthwhile is that our treatment is different from the one in [86] in several respects and we go considerably further regarding the global characterization of the reduced phase space and the completeness of the relevant Hamiltonian flows.…”

Section: A Poisson-lie Deformationmentioning

confidence: 98%

“…Since differences of the 'position variables' p k appear, one feels that this Hamiltonian somehow corresponds to an A-type root system. To better understand the nature of this model, let us now introduce new Darboux variables q k , p k following essentially [86] as…”

Section: A Poisson-lie Deformationmentioning

confidence: 99%

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Integrable many-body systems of Calogero-Ruijsenaars type

Görbe

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This thesis is submitted in accordance with the regulations for the Doctor of Philosophy degree at the University of Szeged. The results presented in the thesis are the author's original work (see Publications) with the exceptions of Section 1.1, which reviews some pre-existing material, and Subsections 4. 2.2, 4.3.1, 4.3.3, 4.3.4, 4.3.5 that contain results obtained by B.G. Pusztai. These are included to make the exposition self-contained.The research was carried out within the Ph.D. programme "Geometric and fieldtheoretic aspects of integrable systems" at the

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Section: A Poisson-lie Deformationsupporting

confidence: 90%

Section: Suthmentioning

confidence: 62%

Section: Suthmentioning

confidence: 93%

Section: A Poisson-lie Deformationmentioning

confidence: 98%

Section: A Poisson-lie Deformationmentioning

confidence: 99%

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Integrable many-body systems of Calogero-Ruijsenaars type

Görbe

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Spectrum and Eigenfunctions of the Lattice Hyperbolic Ruijsenaars–Schneider System with Exponential Morse Term

Diejen¹,

Emsiz²

2015

Ann. Henri Poincaré

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Abstract. We place the hyperbolic quantum Ruijsenaars-Schneider system with an exponential Morse term on a lattice and diagonalize the resulting nparticle model by means of multivariate continuous dual q-Hahn polynomials that arise as a parameter reduction of the Macdonald-Koornwinder polynomials. This allows to compute the n-particle scattering operator, to identify the bispectral dual system, and to confirm the quantum integrability in a Hilbert space set-up.

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Global Description of Action-Angle Duality for a Poisson–Lie Deformation of the Trigonometric $$\varvec{\mathrm {BC}_n}$$ BC n Sutherland System

Fehér

Marshall

2019

Ann. Henri Poincaré

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Integrable many-body systems of Ruijsenaars-Schneider-van Diejen type displaying action-angle duality are derived by Hamiltonian reduction of the Heisenberg double of the Poisson-Lie group SU(2n). New global models of the reduced phase space are described, revealing non-trivial features of the two systems in duality with one another. For example, after establishing that the symplectic vector space C n R 2n underlies both global models, it is seen that for both systems the action variables generate the standard torus action on C n , and the fixed point of this action corresponds to the unique equilibrium positions of the pertinent systems. The systems in duality are found to be non-degenerate in the sense that the functional dimension of the Poisson algebra of their conserved quantities is equal to half the dimension of the phase space. The dual of the deformed Sutherland system is shown to be a limiting case of a van Diejen system.

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A New Model in the Calogero–Ruijsenaars Family

Cited by 12 publications

References 29 publications

Integrable many-body systems of Calogero-Ruijsenaars type

Integrable many-body systems of Calogero-Ruijsenaars type

Spectrum and Eigenfunctions of the Lattice Hyperbolic Ruijsenaars–Schneider System with Exponential Morse Term

Global Description of Action-Angle Duality for a Poisson–Lie Deformation of the Trigonometric $$\varvec{\mathrm {BC}_n}$$ BC n Sutherland System

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