00-433 Iftimovici Andrei
Nonperturbative techniques in the investigation of the spectral properties of many-channel systems (195K, postscript) Nov 7, 00
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Abstract. We show that the $C^*$-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.

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