Vibrational density of states in the disordered solid using classical density functional model

The inhomogeneous density n(x) of an amorphous solid is expressed as a sum of Gaussian profiles. Average width of these profiles represents a characteristic length l signifying the degree of mass localization in the system. We demonstrate that as l spreads beyond a critical value l0, the corresponding vibrational density of states g(ω) deviates from the Debye form gD(ω). We estimate the g(ω) assuming a single peak form similar to the boson peak. For a hard core system of diameter σ we obtain l0≈0.2σ. At an optimum l=lh the boson peak height hB of g(ω) reaches a maximum