Fluctuation-dissipation ratio for compacting granular media

In this paper we investigate the possibility of a dynamical definition of an effective temperature for compacting granular media in the framework of the fluctuation-dissipation (FD) relations. We have studied two paradigmatic models for the compaction of granular media, which consider particles diffusing on a lattice, with either geometrical (tetris model) or dynamical (Kob-Andersen model) constraints. Idealized compaction without gravity has been implemented for the tetris model, and compaction with a preferential direction imposed by gravity has been studied for both models. In the ideal case of an homogeneous compaction, the obtained FD ratio is clearly shown to be in agreement with the prediction of Edwards' measure at various densities. Similar results are obtained with gravity only when the homogeneity of the bulk is imposed. In this case the FD ratio obtained dynamically for horizontal displacements and mobility and from Edwards' measure coincide. Finally, we propose experimental tests for the validity of the Edwards' construction through the comparison of various types of dynamical measurements.