01-449 W. O. Amrein, M. Mantoiu, R Purice

Propagation Properties for Schrodinger Operators Affiliated to Certain C*-Algebras (478K, postscript) Dec 5, 01

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Abstract. We consider anisotropic Schrodinger operators H=P^2+V in L^2(R^n). To certain asymptotic regions F we assign asymptotic Hamiltonians H_F such that (a) the spectrum of H_F is included in the essential spectrum of H and (b) states with energies not belonging to the spectrum of H_F do not propagate into a neighbourhood of F under the evolution group defined by H. The proof relies on C*-algebras techniques. We can treat in particular potentials that tend asymptoticaly to different periodic functions in different cones, potentials with oscillation that decays at infinity, as well as some examples considered before by Davies and Simon in [3].

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