Driven granular media in one dimension: Correlations and equation of state

We study a one-dimensional granular system in which each particle is excited by white noise, with inelastic interactions between the particles. When the coefficient of restitution, eta, is one, the particles are uncorrelated. As eta decreases, long-range correlations between the particles develop. A computer simulation of the system shows a steady-state, power-law particle-particle correlation function, which depends strongly on eta. We give simple analytic arguments for the correlations. We also present an ''equation of state'' for the system of particles, which relates the noise amplitude to the particle density and the average particle speed.