Nonperturbative techniques in the investigation of the spectral properties of many-channel systems

We show that tile C*-algebras generated by the "virtual" hamiltonians of a quantum system (with a qualitatively specified interaction) has in many cases an interesting and nontrivial structure. In particular, the quotient of this algebra with respect to the ideal of compact: operators can be explicitly computed. This allows one to determine in a unified way the essential spectrum and to prove the Mourre estimate for large classes of hamiltonians, including: N-Body systems, stratified media, particles subject to Klaus type interactions (widely separated bumps) and other classes of (phase-space) anisotropic hamiltonians. The results presented here are based on a joint work with V. Georgescu.