On superintegrability of 3D axially-symmetric non-subgroup-type systems with magnetic fields

Abstract

We extend the investigation of three-dimensional (3D) Hamiltonian systems of non-subgroup type admitting non-zero magnetic fields and an axial symmetry, namely the circular parabolic case, the oblate spheroidal case and the prolate spheroidal case. More precisely, we focus on linear and some special cases of quadratic superintegrability. In the linear case, no new superintegrable system arises. In the quadratic case, we found one new minimally superintegrable system that lies at the intersection of the circular parabolic and cylindrical cases and another one at the intersection of the cylindrical, spherical, oblate spheroidal and prolate spheroidal cases. By imposing additional conditions on these systems, we found for each quadratically minimally superintegrable system a new infinite family of higher-order maximally superintegrable systems. These two systems are linked respectively with the caged and harmonic oscillators without magnetic fields through a time-dependent canonical transformation.

12 figures, accepted version

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Cited by in corpus (5)

• New classes of quadratically integrable systems in magnetic fields: the generalized cylindrical and spherical cases
• Higher-order superintegrable momentum-dependent Hamiltonians on curved spaces from the classical Zernike system
• New classes of quadratically integrable systems with velocity dependent potentials: non-subgroup type cases
• Superintegrability and Deformed Oscillator Realizations of Quantum TTW Hamiltonians on Constant-Curvature Manifolds and with Reflections in a Plane
• Superintegrability in the interaction of two particles with spin