Linear response of vibrated granular systems to sudden changes in the vibration intensity

The short-term memory effects recently observed in vibration-induced compaction of granular materials are studied. It is shown that they can be explained by means of quite plausible hypothesis about the mesoscopic description of the evolution of the system. The existence of a critical time separating regimes of ``anomalous'' and ``normal'' responses is predicted. A simple model fitting into the general framework is analyzed in the detail. The relationship between this paper and previous studies is discussed.