Asymptotic analysis of mode-coupling theory of active nonlinear microrheology

TL;DR

This paper develops an asymptotic analysis of a schematic mode-coupling theory model for active nonlinear microrheology, revealing complex transition behaviors and scaling laws near critical points.

Contribution

It introduces a detailed asymptotic framework for understanding force-induced transitions and scaling laws in active nonlinear microrheology within a schematic mode-coupling model.

Findings

Identification of multiple time scales in correlation decay

Power-law regimes in nonlinear friction coefficient

Scaling laws near glass and delocalization transitions

Abstract

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.