Double Inozemtsev limits of the quantum DELL system

Journal Article · 20 January 2022 · Physics Letters. B

DOI: https://doi.org/10.1016/j.physletb.2022.136919 · OSTI ID:1977563

Gorsky, Alexander ^[1]; Koroteev, Peter ^[2]; Koroteeva, Olesya ^[3]; Shakirov, Shamil  ^[4]

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1. Russian Academy of Sciences (RAS), Moscow (Russian Federation); Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
2. University of California, Berkeley, CA (United States); Rutgers University, New Brunswick, NJ (United States)
3. University of Minnesota, Minneapolis, MN (United States)
4. University of Geneva (Switzerland)

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.

• Research Organization: Rutgers University, Piscataway, NJ (United States); University of California, Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC)
• Grant/Contract Number: SC0010008
• OSTI ID: 1977563
• Journal Information: Physics Letters. B, Journal Name: Physics Letters. B Journal Issue: C Vol. 826; ISSN 0370-2693
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English