Neutron scattering evidence on the nature of the boson peak

A close inspection of neutron spectra of glass formers in the frequency region above the boson peak does not show the constant eigenvalue density expected for a random dynamical matrix, but a slow decrease towards higher eigenvalues. In 1,4-polybutadiene and selenium, the slope becomes steeper with increasing temperature in the undercooled liquid, suggesting an influence of the vibrational entropy. One can describe the behaviour quantitatively in terms of a balance between level repulsion (from the randomness of the dynamical matrix) and vibrational entropy. On the basis of this evidence, the boson peak must be a crossover from such a balance at higher frequencies to a mixture of sound waves and additional excitations at low frequency.