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arXiv · 2110.02157

Double Inozemtsev Limits of the Quantum DELL System

Alexander Gorsky·Peter Koroteev·Olesya Koroteeva·Shamil Shakirov
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Abstract

In this letter we study various Inozemtsev-type limits of the quantum double elliptic (DELL) system when both elliptic parameters are sent to zero at different rates, while the coupling constant is sent to infinity, such that a certain combination of the three parameters is kept fixed. We find a regime in which such double Inozemtsev limit of DELL produces the elliptic Ruijsenaars-Schneider (eRS) Hamiltonians albeit in an unconventional normalization. We discuss other double scaling limits and anisotropic scaling of coordinates and momenta. In addition, we provide a formal expression for the eigenvalues of the eRS Hamiltonians solely in terms of their eigenfunctions.

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Alexander Gorsky, Peter Koroteev, Olesya Koroteeva, Shamil Shakirov. 2021-10-05. Double Inozemtsev Limits of the Quantum DELL System. https://doi.org/10.1016/j.physletb.2022.136919

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