Correlation Functions of a Homogeneously Driven Granular Fluid in Steady State

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. The results of computer simulations using an event driven algorithm are compared to the predictions of generalized fluctuating hydrodynamics. The incoherent scattering function ($F_{\rm incoh}(q,t)$) follows time-superposition and is well approximated by a Gaussian $F_{\rm incoh}=\exp \left ( - \frac{q^2}{6} \langle \Delta r^2(t) \rangle \right )$. For sufficiently small wavenumber $q$ we observe sound waves in the intermediate scattering function $F(q,t)$ and in the longitudinal current correlation function $C_l(q,t)$. We determine their dispersion and damping. Temperature fluctuations are predicted to be either diffusive or nonhydrodynamic, depending on wavenumber and inelasticity as characterized by incomplete normal restitution.