The objective of this research is to apply recently developed ideas and techniques from statistical mechanics, plasma physics, and, particularly, dynamical systems theory to problems involving the evolution of self-gravitating systems of objects, both Newtonianly and in general relativity. One general problem to be considered is the "relaxation" and stability of galaxies and galactic nuclei. Two principal aims here are (a) to understand from first principles the origins of the observed similarities amongst galaxies, a nontrivial issue in that the nominal relaxation time tR is typically orders of magnitude larger than the age of the Universe; and related to this, (b) to understand how galaxies respond to strong external stimuli, as provided, e.g., by collisions with other galaxies, by very rapidly evolving towards a new statistical equilibrium. The other area to be considered entails an application of ideas from statistical physics to quantum field theory in the early Universe. Two principal aims here are (a) the modeling of phase transitions and other quantum field theoretic processes as simple stochastic processes and (b) an analysis of particle creation in the early Universe, with the ultimate aim of obtaining an improved understanding of "gravitational entropy" and the observed "arrow of time."
