Low temperature Universalities in amorphous systems: role of microscopic length scales

We find that a competition between dispersion forces among molecules in solids and their phonon mediated coupling leads to a natural length scale based on molecular parameters and relevant to decipher glass anomalies. For amorphous systems, the length scale is of the medium range topological orders and its ratio with the distance of closest approach between molecules turns out to be a constant. This in turn leads to a material independent, constant value of the ratio ${\gamma_l \over \gamma_t}$, with $\gamma_l$ and $\gamma_t$ as the coupling-strength for two amorphous molecules mediated by longitudinal and transverse phonons (also referred as Meissner-Berret ratio) and thereby provides a theoretical explanation of their experimentally obserevd quantitative universality in \cite{mb}. The above length scales are also related to Ioffe-Regel frequency and boson peak frequency of the vibrational spectrum and indicate that the former is of the same order as the latter for transverse phonon-dynamics.