Figure 1

Figure 1: Evolution of the vibrational DOS in a model with disorder in the force constants. The left panel shows the DOS of a simple cubic crystal, analytically calculated, with transverse force constants being a fourth of the longitudinal. The blue curve shows the classic Van Hove singularities (the discontinuities in the DOS). The right panel shows that after introduction of disorder in the force constants, the reduced DOS exhibits a boson peak (pink curve). The histogram is established from numerical calculations of eigenvalues in 25 instances of a 23×23×23 lattice. For details see Ref. [10]. The middle panel shows the evolution of energy levels for interpolations of the dynamical matrix between the two systems. To avoid crowding of the picture, the system size is only 5×5×5 here. The modes lying closest to the transverse acoustic Van Hove singularity are marked in red to allow easier tracing.