Biphonons in quasicrystals

The spectrum of coupled optical biphonon vibrations in quasicrystals with variation of the atom-atom interaction in accordance with the Fibonacci sequence is investigated. For two-phonon states with strong anharmonicity of the vibrations, a system of recursion equations, which is more complicated than the previously employed system for one-phonon states, is obtained. Calculations using this system made it possible to determine the spectrum of biphonon vibrations in a quasicrystal. It is shown that, on the low-frequency edge of the biphonon band, a scaling-type fine structure of the same form as in biphonon spectra of fractal lattices exists in the density of states. It is found that the energy dependence of the density of states is periodic on a logarithmic scale. The period of this dependence is determined. It is noted that the resonance structure in the density of states is of a nonstandard form in the high-frequency region of the biphonon band. Fiz. Tverd. Tela (St. Petersburg) 39, 163–170 (January 1997)