Dependence of relaxation time on effective temperature in driven glasses

Relaxation times of a class of driven glassy systems are shown to depend on a well-defined effective temperature in much the same way that they depend on temperature in quiescent systems. Molecular dynamics simulations were run for two-dimensional systems of bi-disperse spheres interacting via soft repulsive pair potentials. At high density the systems undergo a glass transition as temperature is lowered. We study low-temperature systems driven by an imposed shear gradient in steady state at a fixed high density. Effective temperatures can be defined from fluctuation-dissipation relations by the long-time limit of the ratio of correlation to response. Throughout a range of bath temperatures and shear rates, relaxation times are found to depend only on the bath temperature $T$ and the effective temperature $T_{\rm eff}$. In particular, the relaxation time of the driven system as a function of $T_{\rm eff}$ can be mapped on to the relaxation time of the quiescent system as a function of $T$, using a scale factor that varies only weakly with the ratio $T/T_{\rm eff}$. This suggests that shear unjams the system because it gives rise to a $T_{\rm eff}$ that is higher than the glass transition temperature.