Origin of the effective mobility in non-linear active micro-rheology

TL;DR

This paper clarifies the origins of effective mobility in non-linear active micro-rheology, linking collective effects and thermal fluctuations to better understand particle dynamics in supercooled liquids.

Contribution

It introduces a theoretical framework distinguishing damping and effective mobility, and derives a generalized Stokes-Einstein relation validated by simulations.

Findings

Effective mobility is a collective effect related to the energy landscape.

Thermal fluctuations at long times are characterized by an effective temperature.

The generalized Stokes-Einstein relation accurately predicts diffusion coefficients.

Abstract

The distinction between the damping coefficient and the effective non-linear mobility of driven particles in active micro-rheology of supercooled liquids is explained in terms of individual and collective dynamics. The effective mobility arises as a collective effect which gives insight into the energy landscape of the system. On the other hand, the damping coefficient is a constant that modulates the effect of external forces over the thermal energy which particles have at their disposition to perform Brownian motion. For long times, these thermal fluctuations become characterized in terms of an effective temperature that is a consequence of the dynamic coupling between kinetic and configurational degrees of freedom induced by the presence of the strong external force. The interplay between collective mobility and effective temperature allows to formulate a generalized Stokes-Einstein relation that may be used to determine the collective diffusion coefficient. The explicit relations we deduce reproduce simulation data remarkably well.