Fermi statistics of weakly excited granular materials in a vibrating bed: molecular dynamics simulations

Molecular dynamics simulations were carried out to test the thermodynamic theory of weakly excited, two-dimensional, granular systems [Hayakawa and Hong, Phys. Rev. Lett. 78 (1997) 2764], where granular materials are viewed as a collection of spinless Fermions. We first determine the global temperature T by fitting the steady-state density profile to the Fermi distribution function, and then measure the center of mass, z(T) , and its fluctuations, (Δz(T))2 as a function of T. We find a fairly good agreement between theory and simulations, in particular, in the estimation of the temperature and the scaling behavior of z(T) and (Δz(T))2 .