  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.
