Level dynamics for a periodically driven quantum system

We map the eigenvalue problem of a periodically driven quantum system with N-dimensional Hilbert space to a Hamiltonian N-particle system connected with an infinite-dimensional Lie algebra. This N-particle system is integrable and its equations of motion can be written in Lax form. It is a natural generalization of the so-called generalized Calogero-Moser and Sutherland models, which can be derived from eigenvalue problems of autonomous and kicked quantum systems, respectively. We show that, contrary to common opinion, the generalization of the Weierstrass potential dynamics no longer fulfills all Lax equations and is therefore not expected to be integrable.