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We study the dynamics of a tagged particle in a glassy system under shear.The recently developed integration through transients approach based on modecoupling theory, is continued to arrive at the equations for the taggedparticle correlators and the mean squared displacements. The equations aresolved numerically for a two dimensional system, including a nonlinearstability analysis of the glass solution, the so called beta-analysis. Weperform Brownian Dynamics simulations in 2-D and compare with theory. Afterswitch on, transient glassy correlation functions show strong fingerprints ofthe stress overshoot scenario, including, additionally to previously studiedsuperexponential decay, a shoulder-like slowing down after the overshoot. Wealso find a new type of Taylor dispersion in glassy states which has intriguingsimilarity to the known low density case. The theory qualitatively capturesmost features of the simulations with quantitative deviations concerning theshear induced timescales. We attribute these deviations to an underestimationof the overshoot scenario in the theory.

Tagged-particle motion in glassy systems under shear: Comparison of mode coupling theory and Brownian Dynamics simulations