9421153 Tomsovic This project is aimed at extending new, more powerful semiclassical methods: i) to mesoscopic and atomic problems - the emphasis is on quantum coherence and wave-function localization problems, ii) to simplifying the difficulties arising in connection with chaotic motion, iii) to investigating the leading corrections and higher degrees of freedom, and iv) to adapting the methods to stationary quantum mechanics. Finally, expertise garnered from previous investigations will be brought into the classroom, such as the animation of real time wave equation solutions. The overall subject matter of this proposal is highly interdisciplinary and has consequences in many domains. Analogous phenomena can be found in acoustic, atomic, mesoscopic, molecular and optical systems. It has the further interest of involving the Correspondence Principle and ultimately the interpretation of quantum mechanics. Experience reveals a strong student interest in the combination of mesoscopic physics, nonlinear dynamics and wave asymptotics. Conversant students have a broad base and are well equipped for research careers in a number of disciplines. ***
