The vibrational spectrum of amorphous materials obtained by the use of an Anderson-like Hamiltonian

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Abstract An analytical model, based on an Anderson-like Hamiltonian, is developed in order to describe the vibrational spectrum of amorphous materials. A numerical analysis of the model, performed for the simplest case of a single acoustic-like band, shows the basie features of the vibrational spectrum typical of disordered materials, e.g. the boson peak and a finite line-width of the low-frequency excitations.