Diagrammatic approach to response problems in composite systems

TL;DR

This paper introduces a diagrammatic method to analyze the macroscopic response of composite systems with field-induced forces, emphasizing irreducibility for deriving local property-dependent coefficients.

Contribution

A novel diagrammatic approach is developed to analyze response problems in composite systems, highlighting the role of irreducibility in simplifying macroscopic equations.

Findings

The method effectively describes colloidal suspensions with hydrodynamic interactions.

Irreducibility is shown to be essential for local property-based coefficients.

Diagrammatic analysis simplifies understanding of complex scattering expansions.

Abstract

The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A special diagrammatic method is developed to analyze the structure of the expansion. The concept of irreducibility is discussed in detail and shown to be crucial in obtaining macroscopic equations characterizing the system response with coefficients depending solely on local properties of the medium. Due to the representation of particles by lines in diagrams, irreducibility is given a particularly simple topological interpretation in the diagrammatic language. The method is illustrated by a discussion of response problems in colloidal suspensions in presence of hydrodynamic interactions.