Year: 2025
Type: article
Abstract: We present two superintegrable Hamiltonian systems in two dimensions, defined on the sphere and on the hyperbolic plane. These systems are generalised à la Tremblay-Turbiner-Winternitz (TTW), involving the introduction of a real parameter k > 0, with the aim of extending superintegrable Hamiltonian systems to curved spaces in a way similar to the TTW system on the plane. We carry out both classical and quantum analyses of these new systems. We prove that the superintegrability of the initial systems (i.e. when k = 1) is preserved when k is rational, as in the TTW case. A detailed study of their classical counterparts and trajectories is also included.
Source: Acta Polytechnica
Authors: Mariano A. Del Olmo, Álvaro Romaniega
Institution: Universidad de Valladolid
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: diamond
Funder: Agencia Estatal de Investigación
OpenAlex ID: W4416015483