Stationary state volume fluctuations in a granular medium

A statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles. We periodically fluidize a column of glass beads and find that the sequence of volume fractions phi of post-fluidized states is history independent and Gaussian distributed about a stationary state. The standard deviation of phi exhibits, as a function of phi, a minimum corresponding to a maximum in the number of statistically independent regions. Measurements of the fluctuations enable us to determine the compactivity X, a temperature-like state variable introduced in the statistical theory of Edwards and Oakeshott [Physica A {\bf 157}, 1080 (1989)].