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

Jörg Main, Kirsten Weibert, Vladimir A. Mandelshtam, Günter Wunner
1999 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
Semiclassical spectra weighted with products of diagonal matrix elements of operators A_{alpha}, i.e., g_{alpha alpha'}(E) = sum_n /(E-E_n) are obtained by harmonic 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 required signal lengths to shorter than the Heisenberg time. This implies a significant reduction of the number
more » ... tion of the number of orbits required for periodic orbit quantization by harmonic inversion.
doi:10.1103/physreve.60.1639 pmid:11969926 fatcat:6p2bon6chjfafdlsjs4keyzuxm