## Doctoral Dissertations

Winter 1996

Dissertation

Physics

#### Degree Name

Doctor of Philosophy

We examine the nonequilibrium time evolution of the hadronic plasma produced in a relativistic heavy ion collision, assuming a spherical expansion into the vacuum. We study the O(4) linear $\sigma$ model to leading order in a large-N expansion. Starting in the high temperature unbroken chiral symmetry phase, the system expands and cools, finally settling into the broken symmetry vacuum state. We consider the proper time evolution of the effective pion mass, the order parameter $\langle\sigma\rangle,$ and the particle number distribution. We examine several different initial conditions and look for instabilities (exponentially growing long wavelength modes) which can lead to the formation of disoriented chiral condensates (DCCs). We find that instabilities exist for proper times which are less than 3 fm/c. We also show that an experimental signature of domain growth is an increase in the low momentum spectrum of outgoing pions when compared to an expansion in thermal equilibrium. In comparison to particle production during a longitudinal expansion, we find that in a spherical expansion the system reaches the "out" regime much faster and more particles get produced. However the size of the unstable region, which is related to the domain size of DCCs, is not enhanced.