Introduction to Mode Coupling Theory I

Mode Coupling Theory (MCT) proves to be a successful though idealized approach to describe some phenomena related to the glass transition in supercooled liquids. Close to the transition point correlation functions exhibit a stretched-exponential relaxation and a time-temperature superposition principle, which emerge as natural results of the theory. Furthermore MCT predicted the existence of so called 'attractive glasses', which were found a few years later in local experiments. This first part will comprise a brief motivation, why correlation functions are useful instruments for studying dynamics of liquids on a microscopic scale. The main part will consist of the Zwanzig-Mori projection operator formalism, which allows to derive equations of motion for correlation functions in a systematic way. As for an illustrative application we will glance at the simple fluid and derive the relaxation equation for density fluctuations - the central quantity of interest in MCT.