MPS-RR 2002-26
July 2002

Spectral Theory of Time-Periodic Many-Body Systems

Erik Skibsted

Jacob Schach Møller

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-treshold 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.

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