N-BODY HAMILTONIANS WITH HARD-CORE INTERACTIONS

Abstract

We study N-body hamiltonians with short and long range potentials which are infinite on compact sets of non-zero measure. We show that the generator of the dilation group is locally conjugated to them away from the threshold energies. The notion of conjugacy has to be interpreted in a very weak sense, but this is enough to deduce an optimal form of the limiting absorption principle, and so absence of singular continuous spectrum and local decay. One of the main technical steps of our approach requires a maximal regularity result for the Dirichlet Laplacian in an open set with irregular boundary. We prove it for a large class of non-smooth domains.