HARMONIC VIBRATIONAL EXCITATIONS IN DISORDERED SOLIDS AND THE BOSON PEAK

We consider a system of coupled classical harmonic oscillators with sp atially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerical diagonalization and by applying the single-bond coherent potential approximation. The result s for the density of states g(omega) an in excellent agreement with ea ch other. if the system is near the borderline of stability a low-freq uency peak appears in the quantity g(omega)/omega(2) as a precursor of the instability. We argue that this peak is the analogon of the ''bos on peak,'' observed in structural glasses and other disordered solids. By means of the level distance statistics we show that the peak is no t associated with localized states.