VIBRATIONAL DENSITY-OF-STATES, DYNAMICAL STRUCTURE FACTOR AND EIGENSTATES OF ICOSAHEDRAL MODELS

Extending our previous studies on icosahedral models, we numerically c alculate the integrated density of states (IDOS), the dynamical struct ure factor, and special eigenstates of the ABCK tiling decorated by Da nzer and Talis. We find a broadening of the structure factor at freque ncies where the IDOS exhibits kinks. These kinks arise from a strong i ncrease of the imaginary part of the Green's function (strong damping of plane-wave modes) and indicate localization. The centers of the loc alized vibrations mainly form icosahedra. The occurrence of distinct r egimes in the IDOS may be related to the hierarchical structure of the tiling. The flatness of the optical branches in the dynamical structu re factor implies strong localization of optical modes.