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

TL;DR

This paper derives exact sum rules for the quasi-static and visco-elastic responses of disordered solids at zero temperature, linking non-affine displacements to elastic properties through normal mode analysis.

Contribution

It provides a novel theoretical framework connecting non-affine displacements to elasticity and extends the analysis to visco-elastic dynamical response.

Findings

Quantitative estimates of non-affine correction contributions

Relation between force field correlator and elasticity

Extension of static analysis to visco-elastic response

Abstract

We study exact results concerning the non-affine displacement fields observed by Tanguy et al [Europhys. Lett. {\bf 57}, 423 (2002), Phys. Rev. B {\bf 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.