There are many examples of systems in a state of non- equilibrium in the world around us. Physicists study such systems in the laboratory and observe processes that lead to equilibration. The theoretical studies of such processes led to the discipline of Statistical Mechanics. Early on (1870's) Boltzmann gave us the H-theorem and his famous transport-equation. Though tremendously important this equation is unsatisfactory for some applications, especially for quantum mechanical systems. Using Green's function methods Kadanoff and Baym (1962) developed a set of equations applicable to such systems with the potential of application to numerous technological systems. They reduce in a classical limit to Boltzmann's equation, but are even more complicated. Although frequently referred to, they have in the past been regarded as impractical for numerical solutions. Numerous approximations have however been suggested with applications in plasma-physics, semiconductors and nuclear heavy-ion collisions. Not until recently with the availability of high-speed and large memory computers have exact solutions been possible in certain cases. I have developed computer- programs for the numerical solutions of these equations and am applying them to the study of collisions between heavy ions with emphasis on memory- and correlation- effects. these effects are not included in the Boltzmann-like equations previously applied to these problems. This proposal includes a further study of these effects as well as pionic, relativistic and collective phenomena. The problem of equilibration of a quark-gluon plasma is also included in our studies.
