Introduction to Mode Coupling Theory II

After familiarising ourselves with the framework of the Zwanzig-Mori projection operator formalism, this second part of the introductory seminar to Mode Coupling Theory (MCT) will focus on the central aspects of the theory and some technical details. First of all we introduce the actual mode coupling approxiamtion which leads to a self-consistent set of equations of motion of the density correlation functions. The full set of equations cannot be solved analytically, but expansions in the vicinity of the glass transition point yield already to asymptotic power laws. We will sketch these power laws and show their relation to the dynamics of density correlation function: the von-Schweidler law for intermediate times and the stretched-exponential Kohlrausch function and time-temperature superposition for long times.