Green -Kubo Expression for the shear viscosity of a dense granular fluid.

A system of smooth inelastic hard spheres is considered as a microscopic model for a granular fluid. The standard method of linear response used to obtain exact expressions for hydrodynamic transport coefficients for normal fluids is generalized for this inherently nonequilibrium system. This method is then used to obtain Helfand and Green -- Kubo forms for the shear viscosity of this granular fluid. This expression has the important property that there are no apriori limitations on density or the degree of inelasticity on its domain of validity. Several differences from the corresponding result for normal fluids with continuous potentials and that for elastic hard spheres are noted. Then, some approximate analytical evaluations of this expression are presented and used to make some observations on the mechanisms of momentum transport processes in this fluid.