Contrary to previous studies based on bulk materials, we analyze the behavior of the vibrational density of states (VDOS) and specific heat of an amorphous solid of nano-scales (∼3 nm) at low temperature. With Hamiltonian formulation based on the intermolecular dispersion forces, our analysis indicates a universal semi-circle form of the average VDOS in the bulk of the spectrum along with a super-exponentially increasing behavior in its edge. The latter in turn leads to a specific heat with a superlinear temperature () dependence below< 1even at nano-scales, and, surprisingly agreeing with the experiments although the latter are carried out at macroscopic scales. The omnipresence of dispersion forces at microscopic scales indicates the application of our results to other disordered materials too.
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