Periodic Orbit Quantization of Mixed Regular Chaotic Systems

A general technique for the periodic orbit quantization of systems with near-integrable to mixed regular-chaotic dynamics is introduced. A small set of periodic orbits is sufficient for the construction of the semiclassical recurrence function up to, in principle, infinite length. As in our recent work the recurrence signal is inverted by means of a high resolution spectral analyzer (harmonic inversion) to obtain the semiclassical eigenenergies. The method is demonstrated for the hydrogen atom in a magnetic field. To our knowledge this is the first successful application of periodic orbit quantization in the deep mixed regular-chaotic regime.