Joint eigenfunctions for the relativistic Calogero-Moser Hamiltonians of hyperbolic type. III. Factorized asymptotics

2019/05/30 by Hallnäs, Martin, Ruijsenaars, Simon · 3 citations
#Classical Analysis and ODEs (math.CA) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1905.12918

Abstract

In the two preceding parts of this series of papers, we introduced and studied a recursion scheme for constructing joint eigenfunctions J_N(a₊, a_-,b;x,y) of the Hamiltonians arising in the integrable N-particle systems of hyperbolic relativistic Calogero-Moser type. We focused on the first steps of the scheme in Part I, and on the cases N=2 and N=3 in Part II. In this paper, we determine the dominant asymptotics of a similarity transformed function \rE_N(b;x,y) for y_j-y_j+1→∞, j=1,…, N-1, and thereby confirm the long standing conjecture that the particles in the hyperbolic relativistic Calogero-Moser system exhibit soliton scattering. This result generalizes a main result in Part II to all particle numbers N>3.

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• Baker-Akhiezer specialisation of joint eigenfunctions for hyperbolic relativistic Calogero-Moser Hamiltonians
• Calogero-Sutherland hyperbolic system and Heckman-Opdam \mathfrakgl_n hypergeometric function
• Complex rational Ruijsenaars model. The two-particle case

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