Integrable Systems——Trace Formulas and Inverse-Spectroscopy

Key words: 
• integrable system /
• trace formula /
• inverse spectroscopy

Abstract: Periodic orbits of two dimensional uncoupled quartic oscillator were calculated by inte grating Hamiltonian equations of motion on reasonable tori, and several classical quantities were also computed. Inserting them into Berry Tabor trace formula, a trace, i.e., the semiclassical density of states of the corresponding quantum system, was obtained. Finally, Fourier transform was adopted to verify the contribution of each periodic orbit. Good agreement between the semiclassical ...