9412706 Sundaram The focal point of this research proposal is the understanding of the use, efficacy and limitations of classical and semi-classical methods in describing the dynamics of strongly coupled quantum systems. Since the strength of the interaction precludes the use of quantum perturbation theory in these systems, non-perturbative intuition is derived from a classical description of the dynamics, which is most often nonintegrable or chaotic. A number of important issues of both practical and formal consequence arise from the quantization of dynamics with a classically chaotic limit. In particular, we propose to investigate 1) the periodic orbit expansion starting from exact expressions of the trace of quantum propagators, the contributions of analytically continued orbits and the possibility of conherence (scarred wave functions) associated with these so-called 'ghost' orbits,2) the effects of noise introduced via parametric fluctuations on de stabilizing scarred wave-functions and 3) scarred wave functions in higher dimensions with specific application to the problems of stabilization of ground state atoms in super-intense laser fields and to the noise spectroscopy in the interaction of Rydberg atoms with microwaves. ***
