Order and Chaos in Classical and Quantum Mechanics

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Research is proposed on semiclassical methods for calculating the behavior of quantumsystems whose classical counterparts are chaotic. The primary focus will be on breakup of anexcited complex. Of particular interest is the study of the ionization of atoms in electric andmagnetic fields. If an atom is excited by a single-photon process from a strongly bound state bya short-pulse laser, A + hv = A*, and then the excited state decays, A* = A+ + e-, it is possible tomeasure the time between the laser pulse and the appearance of an electron at a detector. Suchmeasured "time spectra" do not show exponential decay; instead, electrons appear at the detectorin a train of pulses. These pulses are related to classical orbits of the electron. Calculationsbased upon classical mechanics indicate that these chaotic pulse-trains are described by a kind offractal. We are analyzing the structure of such fractals and making predictions of results offuture experiments.In addition we will continue to apply closed-orbit theory to atomic spectra. There arenew experimental measurements in several laboratories, and we will help to provide theoreticalinterpretation of these measurements.