*** 9610501 HELLER The Theoretical and Computational Ahemistry program is supporting Professor Eric Heller at Harvard University to work on scattering theory. First, Heller will take a new look at scattering theory at extremely low energies. This regime has become important because of laser cooling and trapping of atoms, as well as carrier gas cooling and trapping of molecules. In this "cold collision" regime, Heller will study ultra-low energy, three-atom collisions and recombination (molecule formation), proximity resonances, which are a new class of low energy multiple scattering resonances related to Efimov states, and ultra-low energy molecule-molecule collisions, with an eye to the formation of long lived resonances. Common to these areas is the concept of "boundary condition engineering," wherein the effect of short range potentials can in fact be ascribed to a change in boundary conditions on the wavefunction. In a related study Heller will extend and apply the theory of multiple scattering and conductance in "quantum corrals" and other arrangements or arrays of atoms into walls and sheets. He will also investigate novel approaches to dynamical tunneling in polyatomic molecules, and its effect on high resolution spectra, deflection of beams in inhomogeneous fields, and quantum control in Landau-Zener crossing. This work, like the ultra-low energy scattering theory above, addresses the extreme quantum regime. In a second class of problems, at the opposite end of the scale at higher energy, Heller will extend his fundamental research in semiclassical approximations to chaotic systems to include the theory of scarring by classical periodic orbits and semiclassical quantization of chaos. In particular he is looking for an appropriate nonlinear theory of wavefunction scarring. Finally this work will undertake several projects involving fundamental issues of quantization, including quantization on constrained non-Euclidian spac es, and quantization of chaos in maps such as the whisker map. This research involves fundamental studies of quantum mechanics, and the profound effects quantum mechanics has on matter, as energy is lowered almost to absolute zero. At very low temperatures, matter wave-like behavior dominates over particle-like behavior. Wavelengths get extremely long. The waves have to obey "boundary conditions," which are rules on how the waves behave when one atom or molecule approaches another, or approaches a wall. At ultra-low energies these boundary conditions are uncommonly important, often determining the way the matter behaves. In this strange "tail wagging the dog" regime, anything that can be done to change the boundary conditions may have profound effects. For example, normal boundary conditions in quantum mechanics forces minimum energy upon the system known as the zero point energy. Removing the zero point energy, by using walls made of special atoms, may drastically affect the usefulness of small devices such as wires, and may profoundly affect the outcome of the slow collision of two cold molecules. Related work involves the issue of quantization; that is, how do we take a given system and correctly endow it with the proper quantum behavior. There are rules on how to do this in simple cases but the rules are ambiguous when constraints are present, for example (requiring that a given bond length to be a certain fixed value). Heller is developing some ideas which bootstrap the ambiguous cases as limits of the easy cases, thus removing the ambiguity. ***
