Boson peak in confined disordered systems

The vibrational density of states (VDOS) of disordered systems shows a low-frequency excess, the so-called boson peak. Experiments show a change in the shape of the boson peak when the systems are spatially confined. Depending on the type of confinement (hard or soft) the low-frequency wing of the boson peak is either suppressed or enhanced. Here, a simple model, a crystalline system with disordered nearest-neighbor force constants, is studied with boundary conditions mimicking the confinement. The VDOS calculated by numerical diagonalization shows qualitatively the same confinement effect as the experiment. In this model, the effect is a consequence of modes of the bulk system being shifted up or down for hard and soft confinement, respectively. A simple rescaling procedure is suggested to convert the VDOS of the bulk into that of the confined system.