Semiclassical spectra and diagonal matrix elements by harmonic inversion of cross-correlated periodic orbit sums

Semiclassical spectra weighted with products of diagonal matrix elements of operators (A) over cap(alpha), i.e., g(alpha alpha')(E) = Sigma n[n\(A) ov er cap(alpha)\n][n\(A) over cap(alpha')\n]/(E-E-n), are obtained by harmoni c inversion of a cross-correlation signal constructed of classical periodic orbits. The method provides highly resolved semiclassical spectra even in situations of nearly degenerate states, and opens the way to reducing the r equired signal lengths to shorter than the Heisenberg time. This implies a significant reduction of the number of orbits required for periodic orbit q uantization by harmonic inversion. [S1053-651X(99)07908-8].