High Resolution Quantum Recurrence Spectra: Beyond the Uncertainty Principle

Highly resolved recurrence spectra are obtained by harmonic inversion of quantum spectra of classically chaotic systems and compared in detail to the results of semiclassical periodic orbit and closed orbit theory. Our analysis is sensitive to separate orbits with nearly degenerate recurrence periods and uncovers complex (“ghost”) orbits even when they are hidden behind close-by real orbits. The method is demonstrated on an example of the hydrogen atom in external magnetic and electric fields, for both the density of states and the quantum photoabsorption cross section.