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Harmonic Vibrational Excitations in Disordered Solids and the “Boson Peak”

Harmonic Vibrational Excitations in Disordered Solids and the “Boson Peak”

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement …