This grant is to support studies of quantum systems that display regular and irregular classical trajectories with the aid of various semiclassical methods, some traditional and some very recently developed. In the first year, attention will be focused on highly excited atoms in strong external fields. At low energies and weak fields, these systems show quasiperiodic trajectories, and semiclassical energies and wavefunctions can be calculated by quantization of action variables. For high energies or strong fields, the trajectories are chaotic and familiar methods cannot be used. A theory is being developed that shows that orderly fluctuations in transition amplitudes are associated with closed orbits of such systems.
