Violation of the Einstein relation in granular fluids: the role of correlations

We study the linear response in diff. erent models of driven granular gases. In some situations, even if the velocity statistics can be strongly non-Gaussian, we do not observe appreciable violations of the Einstein formula for diff. usion versus mobility. The situation changes when strong correlations between velocities and density are present: in this case, although a form of. fluctuation-dissipation relation holds, the differential velocity response of a particle and its velocity self- correlation are no longer proportional. This happens at high densities and strong inelasticities, but still in the. fluid- like ( and ergodic) regime.