Glassy systems under time-dependent driving forces: Application to slow granular rheology - art. no. 051302

We study the dynamics of a glassy model with infinite range interactions ex ternally driven by an oscillatory force. We find a well-defined transition in the (temperature-amplitude-frequency) phase diagram between (i) a "glass y'' state characterized by the slow relaxation of one-time quantities, agin g in two-time quantities and a modification of the equilibrium fluctuation- dissipation relation; and (ii) a ''liquid'' state with a finite relaxation time. In the glassy phase, the degrees of freedom governing the slow relaxa tion are thermalized to an effective temperature. Using Monte Carlo simulat ions, we investigate the effect of trapping regions in phase space on the d riven dynamics. We find that it alternates between periods of rapid motion and periods of trapping. These results confirm the strong analogies between the slow granular rheology and the dynamics of glasses. They also provide a theoretical underpinning to earlier attempts to present a thermodynamic d escription of moderately driven granular materials.