Universality of Ultrasonic attenuation in amorphous systems at low temperatures

TL;DR

This paper presents a theoretical explanation for the universal behavior of ultrasonic attenuation in amorphous materials at low temperatures, linking it to molecular dynamics and length-scale ratios.

Contribution

It introduces a random matrix model of the Hamiltonian to explain the universality of ultrasonic attenuation across different amorphous systems.

Findings

Ultrasonic attenuation coefficient is expressed as a ratio of two length-scales.

The ratio remains constant across various materials, explaining universality.

The model aligns with experimental observations at low temperatures.

Abstract

The competition between unretarded dispersion interactions between molecules prevailing at medium range order length scales and their phonon induced coupling at larger scales leads to appearance of nano-scale sub structures in amorphous systems. The complexity of intermolecular interactions gives rise to randomization of their operators. Based on a random matrix modelling of the Hamiltonian and its linear response to an external strain field, we show that the ultrasonic attenuation coefficient can be expressed as a ratio of two crucial length-scales related to molecular dynamics. A constant value of the ratio for a wide range of materials then provides a theoretical explanation of the experimentally observed universality of the ultrasonic attenuation coefficient at low temperatures.