Energy fluctuation, diffusivity and mobility in a 2D vibrated granular packing*

We present an experimental realization of a 2D vibrated granular packing. The new agitation method allows a spatially non synchronized influx of energy and the study of the vibrated packing at steady state. By image analysis of fast-camera movies, we obtain the velocity fluctuation spectra at different vertical levels and then, we separate the agitation velocities from the velocity fluctuations corresponding to the ``thermalized'' degrees of freedom. By measuring the corresponding particle diffusivities, we show that, in spite a large heterogeneity and anisotropy of the vibration, a relation between diffusivity and ``thermalized'' kinetic energy can be identified. We relate this type of fluctuation-dissipation relation to the mobility of macroscopic intruders of different sizes and weight moving in the vibrated granular packing.