Microrheology considering parallel relaxation channels

Rheology is the study of the flow of matter. Microrheology extends rheology to a microscopic scale by observing the motion of a microscopic tracer particle. This reduces the required amount of the sample and additionally provides information about the local viscoelastic properties. Microrheology is called active, when the tracer is moved by means of an external force. This allows to probe the nonlinear regime of the rheological quantities, i.e. when the viscosity becomes a function of the applied force. However, the relation of micro- and macrorheological quantities is not yet fully understood.A mode coupling theory (MCT) for active microrheology has been developed by Gazuz et al. We extend this model for systems of hard spheres to higher forces. The novel approach is to decompose the memory kernel into parallel relaxation channels. In this thesis we will elaborate this new model. First, we give a derivation of the MCT equations of motion for the tracer density mode correlator. Throughout this thesis we will focus on the the long time limit of this quantity, also called tracer nonergodicity parameter. This quantity is only nonzero, when we are in the glassy state, i.e. the tracer remains localized for all times. We develop and implement a discretization scheme for the numerical solution of the long time limit. We propose several methods to find the critical force, where a delocalization transition of the tracer particle occurs and compare their results. Furthermore, we analyze the characteristics of the nonergodicity parameter. We find that the mean as well as the mean squared displacement increase strongly near the critical force. The reason for this is the evolution of an exponential tail in direction of the applied force in the probability distribution of the tracer particle. We propose a simple model to explain this tail. Finally, we can identify this feature also in the Fourier space solution