Propagation Estimates for Two-cluster Scattering Channels of N-body Schr\"odinger Operators

Abstract

In this paper we prove propagation estimates for two-cluster scattering channels of N-body Schr\"odinger operators. These estimates are based on the estimate similar to Mourre's commutator estimate and the method of Skibsted. We also obtain propagation estimates with better indices using projections onto almost invariant subspaces close to two-cluster scattering channels. As an application of these estimates we obtain the resolvent estimate for two-cluster scattering channels and microlocal propagation estimates in three-body problems without projections. Our method clearly illustrates evolution of the solutions of the Schr\"odinger equation.