The Fermi Statistics of 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, 2764(1997)] where granular particles are treated as spinless Fermions. The density profile is measured and then fit to the Fermi distribution function, from which the global temperature of the system, $T$, is determined. Then the center of mass, $$, and its uctuations, $< z(T)^2 >$, are measured and plotted as functions of $T$. The Fermi function fits the density profile fairly well, with the value of $T$ being fairly close to the predicted value. The scaling behavior of $< z(T) >$ and $< z(T)^2 >$ is in fairly good agreement with the theory.