  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, 2764 (1997)], 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, <(\Delta
z(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 <(\Delta z(T))^2>.
