Jacob Schach Moller and Erik Skibsted
Spectral theory of time-periodic many-body systems
(221K, amstex)

ABSTRACT.  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.