Quantum chaos and the limits of semiclassical prediction

Spectral features and eigenfunctions of the kicked rotor are contrasted with those obtained in the semiclassical limit. For extended eigenfunctions, the difference in the spectra scales as (h) over bar(3/2) in the random matrix theory limit and eigenvalues can be uniquely identified. However, for dynamically localized eigenfunctions, the semiclassical spectrum does not resemble the exact spectrum though numerics indicate that statistical features are reproduced. We suggest that semiclassical periodic orbit theory, even with improved asymptotics, will only provide a statistical description of dynamical localization.