Analysis of magneto-oscillatory spectra in cuprous oxide, with classical "quasi-closed" unstable trajectories

A quantum manifestation of classical non-integrability is found and analyze d in solid state spectroscopy. Magneto-oscillatory spectra in cuprous oxide are observed and attributed to classical unstable trajectories of the syst em of magnetized hydrogen-type atom which has long been a prototype of non- integrable system. Classical trajectories are numerically calculated with v arious initial conditions, and it is found that quasi-closed trajectories c ontribute to the spectrum. The resultant trajectories are sorted in three g roups according to their recurrence frequencies (quasi-period). The three q uasi-periods are shown to be corresponding to the characteristic three peak s of the auto-correlation function of photon absorbed excitonic state. This novel method for assignment using quasi-closed unstable trajectories has i mplications on complex spectrum remained unclear.