Spectral theory of time-periodic many-body systems

We study the spectrum of the monodromy operator for an N-body quantum system in a time-periodic external field with time-mean equal to zero. This includes AC-Stark and circularly polarized fields, and pair potentials with a local singularity up to (and including) the Coulomb singularity. In the framework of Floquet theory we prove a local commutator estimate and use it to prove a Limiting Absorption Principle for the Floquet Hamiltonian as well as exponential decay estimates on non-threshold eigenfunctions. These two results are then used to obtain a second-order perturbation theory for embedded eigenvalues. The principal tool is a new extended Mourre theory.