Nonclassical paths in the recurrence spectrum of diamagnetic atoms

Using time-independent scattering matrices, we study how the effects of nonclassical paths on the recurrence spectra of diamagnetic atoms can be extracted from purely quantal calculations. This study reveals an intimate relationship between two types of nonclassical paths: exotic ghost orbits and diffractive orbits. This relationship proves to be a previously unrecognized reason for the success of semiclassical theories, such as closed-orbit theory, and permits a comprehensive reformulation of the semiclassical theory that elucidates its convergence properties.