Double Inozemtsev Limits of the Quantum DELL System
arXiv:2110.02157 · doi:10.1016/j.physletb.2022.136919
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.
14 pages, 4 figures
References in corpus (7)
- Defects and Quantum Seiberg-Witten Geometry
- Hofstadter's Butterfly in Quantum Geometry
- BPS/CFT correspondence V: BPZ and KZ equations from qq-characters
- Duality in elliptic Ruijsenaars system and elliptic symmetric functions
- Seiberg-Witten curves and double-elliptic integrable systems
- New non-linear equations and modular form expansion for double-elliptic Seiberg-Witten prepotential
- Characteristic determinant and Manakov triple for the double elliptic integrable system