Sum rules for the quasi-static and visco-elastic response of disordered solids at zero temperature

We study exact results concerning the non-affine displacement fields observed by Tanguy et al. [Europhys. Lett. 57, 423 (2002), Phys. Rev. B 66, 174205 (2002)] and their contributions to elasticity. A normal mode analysis permits us to estimate the dominant contributions to the non-affine corrections to elasticity and relate these corrections to the correlator of a fluctuating force field. We extend this analysis to the visco-elastic dynamical response of the system.