Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars) - INSPIRE

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Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an appendix by S. Ruijsenaars)

Bela Gabor Pusztai
(
- Szeged U. and
- Wigner RCP, Budapest
)

Jan 30, 2017

60 pages

Published in:

Commun.Math.Phys. 359 (2018) 1, 1-60

Published: Dec 16, 2017

e-Print:

1701.08558 [math-ph]

DOI:

10.1007/s00220-017-3035-2

View in:

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Abstract: (Springer)

In this paper, we construct global action-angle variables for a certain two-parameter family of hyperbolic van Diejen systems. Following Ruijsenaars’ ideas on the translation invariant models, the proposed action-angle variables come from a thorough analysis of the commutation relation obeyed by the Lax matrix, whereas the proof of their canonicity is based on the study of the scattering theory. As a consequence, we show that the van Diejen system of our interest is self-dual with a factorized scattering map. Also, in an appendix by S. Ruijsenaars, a novel proof of the spectral asymptotics of certain exponential type matrix flows is presented. This result is of crucial importance in our scattering-theoretical analysis.

Note:

48 pages

self-duality
scattering
pair: Lax
commutation relations
spectral
translation

References(74)

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