Abstract

Vibrational properties of a Cayley-tree-type system are investigated: Normal modes and squared frequency spectral densities are calculated for infinite homogeneous monatomic and diatomic Cayley trees. Effect of an impurity is then investigated. Existence of a virtual localized mode is thereby discussed with emphasis. Eigenfrequencies and eigenfunctions of a spherical Cayley tree of finite size are also calculated. Then the spectral density of the infinite homogeneous Cayley tree and that of the spherical Cayley tree in the large limit size are compared, and the relation between these two systems is discussed.