Noise induces rare events in granular media

The granular Leidenfrost effect (B. Meerson et al, Phys. Rev. Lett. {\bf 91}, 024301 (2003), P. Eshuis et al, Phys. Rev. Lett. {\bf 95}, 258001 (2005)) is the levitation of a mass of granular matter when a wall below the grains is vibrated giving rise to a hot granular gas below the cluster. We find by simulation that for a range of parameters the system is bistable: the levitated cluster can occasionally break and give rise to two clusters and a hot granular gas above and below. We use techniques from the theory of rare events to compute the mean transition time for breaking to occur. This requires the introduction of a two-component reaction coordinate.