Collective spectrum of coherent crystals

The spectrum of collective excitations of the coherent crystals (CC's) [1, 2] is investigated for some simple models. The parts of the spectrum with the momenta near zero and near the vectors of the reciprocal lattice correspond to the following two kinds of the sound: a “liquid” sound (representing mainly the density oscillations at fixed lattice) and a “solid” one (mainly the lattice oscillations) and also to the short-wave density oscillations containing, in particular, the wave-lengths shorter than the lattice period. The latter kind excitations may be interpreted as the long-wave oscillations of the lattice amplitude (with the “plasmon” character of the wave-length dependence on the frequency).