EFFECTIVE MEDIUM APPROXIMATION FOR VIBRATIONAL EXCITATIONS IN DISORDERED SOLIDS

The effective medium approximation (EMA) was applied to the investigation of the vibrational properties of disordered solids. EMA calculations were performed for models characterized by a continuous distribution of force constants and compared with calculations for a model with fractal topology characterized by a binary distribution of force constants. In all models, a strong derivation from the usual Debye-omega-2 law above a certain frequency omega-1 was found in the vibrational density of states. Experimental results for silica aerogels are used to discuss the relevance of our theory to this type of material.