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

Abstract

Semiclassical spectra weighted with products of diagonal matrix elements of operators A_{alpha}, i.e., g_{alpha alpha'}(E) = sum_n <n|A_{alpha}|n><n|A_{alpha'}|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.

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

References in corpus (3)

• Harmonic inversion as a general method for periodic orbit quantization
• hbar expansion for the periodic orbit quantization by harmonic inversion
• Semiclassical Non-Trace Type Formulas for Matrix Element Fluctuations and Weighted Densities of States

Cited by in corpus (7)

• Decimation and Harmonic Inversion of Periodic Orbit Signals
• Semiclassical quantization of the hydrogen atom in crossed electric and magnetic fields
• Photoabsorption spectra of the diamagnetic hydrogen atom in the transition regime to chaos: Closed orbit theory with bifurcating orbits
• Semiclassical Non-Trace Type Formulas for Matrix Element Fluctuations and Weighted Densities of States
• The hydrogen atom in an electric field: Closed-orbit theory with bifurcating orbits
• Periodic orbit quantization of chaotic systems with strong pruning
• Classical, semiclassical, and quantum investigations of the 4-sphere scattering system