Kinetic theory of hydrodynamic response functions for a dense granular fluid

The general response functions characterizing the response of a homogeneous isolated granular fluid to small spatial perturbations in the hydrodynamic fields have been described recently [1]. These response functions are time correlation functions for the Homogeneous Cooling State. Special cases of this class of time correlation functions are the Green - Kubo expressions for the hydrodynamic transport coefficients. In this work, these functions are expressed in terms of reduced singe particle functions that are expected to obey a linear kinetic equation. The functional assumption required to obtain such a kinetic equation and its relationship to the well studied Boltzmann and Enskog kinetic theories of a granular fluid are illustrated in the particular context of the shear viscosity of this fluid. [1] J. W. Dufty, A. Baskaran and J. J. Brey, J. Stat. Mech. L08002 (2006).