Oscillations of a molecular dusty-plasma crystal

The phonon spectra of a two-layer plasma crystal are analyzed. A simple model describing nonreciprocal forces acting between dust grains is formulated. General trends in the dynamics of a single dust molecule consisting of two vertically aligned grains are described. An integral of motion analogous to energy is found in the harmonic approximation. The conditions allowing the existence of a molecular crystal for which interaction between pairs of grains weakly affects the state of an individual molecule are determined. The oscillation spectra are obtained in an explicit form.