BRANCHED STRUCTURE OF VIBRATION SPECTRUM OF DIAMOND TYPE HIERARCHICAL LATTICES

In this letter the spectral structure of lattice vibrations of diamond type hierarchical lattices is studied. A novel feature is found that spectra form a branched structure associated with generations, in contrast with that of other regular fractals. We point out that it seems to be difficult to get a single spectral dimension to describe the scaling behaviour of the low-frequency density of states.