Isotropic tensor fields in amorphous solids: Correlation functions of displacement and strain tensor fields

TL;DR

This paper extends the mathematical framework for isotropic tensor fields to arbitrary dimensions and applies it to analyze correlation functions of displacement and strain in amorphous solids, revealing complex distribution behaviors and non-monotonic correlations.

Contribution

It generalizes the theory of isotropic tensor fields to any dimension and applies it to amorphous solids, providing new insights into strain correlations and distribution properties.

Findings

Strain components in reciprocal space follow a complex circularly-symmetric Gaussian distribution.

Non-Gaussian effects become visible at large wavenumbers q.

Dynamical strain correlation functions are non-monotonic with respect to q.

Abstract

Generalizing recent work on isotropic tensor fields in isotropic and achiral condensed matter systems from two to arbitrary dimensions we address both mathematical aspects assuming perfectly isotropic systems and applications focusing on correlation functions of displacement and strain field components in amorphous solids. Various general points are exemplified using simulated polydisperse Lennard-Jones particles in two dimensions. It is shown that the strain components in reciprocal space have essentially a complex circularly-symmetric Gaussian distribution albeit weak non-Gaussianity effects become visible for large wavenumbers q where also anisotropy effects become relevant. The dynamical strain correlation functions are strongly non-monotonic with respect to q with a minimum roughly at the breakdown of the continuum limit.