Semiclassical Spectra and Diagonal Matrix Elements by Harmonic Inversion of Cross-Correlated Periodic Orbit Sums

Details Semiclassical Spectra and Diagonal Matrix Elements by Harmonic Inversion of Cross-Correlated Periodic Orbit Sums Semiclassical Spectra and Diagonal Matrix Elements by Harmonic Inversion of Cross-Correlated Periodic Orbit Sums

1998-04-14

arxiv.org/abs/chao-dyn/9804025v2

Phys. Rev. E 60 (1999) 1639

Nonlinear Sciences

Chaotic Dynamics

5 pages, 1 figure, REVTEX, revised manuscript submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.60.1639

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 of orbits required for periodic orbit quantization by harmonic inversion.

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