The goal of this proposal is to study the dynamics of a variety of quantum systems ranging from a dense gas of very hot pions, to that of an extremely cold, Bose-Einstein condensed, atomic vapor. The common denominator of these systems is that they all obey the Bose-Einstein statistics and can be simulated numerically using very efficient, newly developed algorithms by this investigator. The importance of these studies is that they can tell us how matter behaves under very extreme circumstances. In the case of pions, which are created in ultra high energy collisions of large nuclei, such as gold or uranium, their collective excitations reveal ways in which a basic symmetry of nature is restored at high tempearature. Such a high temperature occurs nowhere else naturally except during the early Big-Bang formation of the universe. In Bose-Einstein condensations, a single quantum state is occupied by a macroscopic number of particles. Thus the very fine details of a quantum state can be magnified a million-billion-billion times. The exploitation of this occupation can in principle be used to make exceedingly high precision measurments.
