Fermi statistics applied to a weakly excited column of granular particles in a vibrating bed

A one-dimensional experiment in granular dynamics is carried out to test the thermodynamic theory of weakly excited granular systems [Hayakawa and Hong, Phys. Rev. Lett. 78 (1997) 2764] where granular particles are treated as spinless Fermions. The density profile is measured and then fit to a granular Fermi distribution function, from which the global temperature of the system, T, is determined. Then the center of mass, 〈z(T)〉, and its fluctuations, 〈Δz(T)2〉, are measured and plotted as functions of T. The granular Fermi function fits the density profile fairly well, with the value of T being reasonably close to the predicted value. The scaling behavior of 〈z(T)〉 and 〈Δz(T)2〉 is in excellent agreement with the theory.