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

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 where isotropy may not hold. Various general points are exemplified using simulated polydisperse Lennard-Jones particles. 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 wave numbers q where also anisotropy effects become relevant. The dynamical strain correlation functions are strongly nonmonotonic with respect to q with a minimum roughly at the breakdown of the continuum limit.