LATTICE VIBRATION ON PSEUDO-LATTICES

Vibrational properties on pseudo-lattices called diatomic Bethe lattic es and diatomic spherical Cayley tree lattices are studied. First, the squared frequency density and normal modes are calculated by the Gree n's function method for the Bethe lattice. Next, the frequency spectru m and eigenmodes of the spherical Cayley tree lattice in the large lim it size are investigated to compare with those of the Bethe lattice. T he vibrational modes on the Bethe lattice are shown to be only spheric ally symmetric and the minor modes of the spherical Cayley tree lattic e in the large limit size. Comparison of vibrational properties of the previously studied monatomic pseudo-lattices with those of the presen t ones with mio kinds of masses shows a remarkable similarity in mathe matical structure through a dispersion relation.