The Fermi Statistics of a Weakly Excited Particle 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, $<z(T)>$, and its fluctuations, $< \Delta z(T)^2 >$,aremeasuredandplottedasfunctionsof$T$. The 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 $<\mathrm{\Delta }z(T{)}^2>$ is in excellent agreement with the theory.