Universality of Ultrasonic attenuation in amorphous systems at low temperatures
arXiv:2009.00556
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.
40 Pages (double spacing), 5 figures