The anisotropic glassy properties of quasicrystals within an amended tunneling model

TL;DR

This paper extends the tunneling model to explain anisotropic sound absorption in decagonal quasicrystals by considering an ensemble of oriented two-level systems and analyzing their coupling tensors and distributions.

Contribution

It introduces an extended tunneling model with tensorial coupling to account for anisotropic properties in quasicrystals, incorporating symmetry considerations and distribution analysis.

Findings

Distribution of TLS coupling elements is complex and non-intuitive.

The model captures anisotropic sound absorption behaviors.

Tensor structure reflects quasicrystal symmetry.

Abstract

We use an extended version of the standard tunneling model to explain the anisotropic sound absorption in decagonal quasicrystals. The glassy properties are determined by an ensemble of two level systems (TLS), arbitrarily oriented. The TLS is characterized by a $3\times3$ symmetric tensor, which couples to the strain field through a $3\times3\times3\times3$ tensor of coupling constants, $[[R]]$. The structure of $[[R]]$ reflects the symmetry of the quasicrystal. We also analyze the probability distributions of the elements of $[T]$ in this particular model for a better understanding of the characteristics of "isotropic" and "anisotropic" orientations distributions of the ensemble of TLSs. We observe that the distribution of the elements is neither simple, nor intuitive and therefore it is difficult to guess it a priory, using qualitative arguments based on the symmetry properties.