An explicitly solvable model with classical resonant scattering

摘要

We consider one-dimensional classical scattering on a finite quadratic potential. we demonstrate exponen- tial decay of correlation functions and calculate the power spectrum. The generalized spectral decomposition of the Liouville operator in the test space of real analytic, fast decreasing functions is obtained. It is chown that the generalized eigenvalues are the poles of the resolvent on the second she4et, and the generalize eigenprojectors are the residues of these poles.