Dispersive charge transfer model with long-range quantum interactions
The author proves long-range asymptotic completeness for the dispersive charge transfer model, i.e., for a quantum particle in the field of \(N\) classical particles following assigned trajectories, where the dispersion relation of the quantum particle may be taken from a fairly large class of elliptic symbols containing the relativistic \(p(\xi)=(| \xi| ^2+1)^{1/2}\). This is a continuation of the author's work on scattering for the charge transfer model which he previously studied in the case of short-range interactions. His result may be regarded as a step toward proving asymptotic completeness for relativistic \(N\)-particle quantum systems. For the proof recent methods from \(N\)-particle quantum scattering such as propagation estimates are employed. Previously the charge transfer model was investigated, e.g., by Yashima, Hagedorn, Wüller, and Graf.
scientific article; zbMATH DE number 1115459
scientific article