Collective excitations in an array of compensated dislocations

Collective vibrational excitations that arise in an array of compensated dislocations because of long-range elastic fields related to nonuniform dislocation polarization are considered. Dispersion relations are derived analytically. It is shown that there are two, for screw dislocations, and three, for edge dislocations, branches of collective excitation. In both cases, one of the branches is characterized by a threshold frequency depending on the dislocation density.