Asymptotic analysis of mode-coupling theory of active nonlinear microrheology

Details Asymptotic analysis of mode-coupling theory of active nonlinear microrheology Asymptotic analysis of mode-coupling theory of active nonlinear microrheology

2012-04-11

arxiv.org/abs/1204.2407v1

Physics

Condensed Matter

Soft Condensed Matter

17 pages, 12 figures

Scientific paper

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 steady-state velocity by locally melting the glass. Asymptotic expressions for the transient density 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 correlators. For the nonlinear friction coeffcient of the probe, the asymptotic expressions cause various regimes of power-law variation with the external force, and two-parameter scaling laws.

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