Space-resolved stress correlations and viscoelastic moduli for polydisperse systems: two faces of the stress noise

We discuss several advances in the theory of space-resolved stress correlations and viscoelastic relaxation moduli for liquids and other amorphous systems. Our study focuses on three aspects: (i) For a given wavevector q̲ the q̲-dependent longitudinal (parallel to q̲) and transverse (perpendicular to q̲) viscoelastic moduli of a fluid relax to equilibrium values in the long time limit t → ∞. We derive relations for the q̲-dependent equilibrium moduli in terms of generalized structure factors, which are valid for systems with mass polydispersity. (ii) We revisit an earlier derivation of the relation between the q̲-dependent tensors of viscoelastic relaxation moduli (E) and stress correlations (C), which employed the concept of the "stress noise", but was also hinged on consideration of non-stationary flows. The new derivation of the C-E relation presented here is based on a conceptually simple argument avoiding non-stationary processes. (iii) We discuss the relevance of the mass current field for the q̲-dependent viscoelastic relaxation moduli and the general relations between these moduli and correlation functions of the stress noise.