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Asymptotic analysis of mode-coupling theory of active nonlinear microrheology
Manuel Gnann and Thomas Voigtmann
We discuss a schematic model of mode-coupling theory for force-driven active nonlinear microrheology, where a single probe particle is pulled by a constant external force through a dense host medium. The model exhibits both a glass transition for the host, and a force-induced delocalization transition, where an initially localized probe inside the glassy host attains a nonvanishing steadystate velocity by locally melting the glass. Asymptotic expressions for the transient correlation functions of the schematic model are derived, valid close to the transition points. There appear several nontrivial time scales relevant for the decay laws of the correlator. For the nonlinear friction coefficient of the probe, the asymptotic expressions give rise to two-parameter scaling laws.