The normal mode spectrum in a two-dimensional lattice of neutral atoms

The acoustic phonon spectrum in a two-dimensional lattice composed of neutral atoms is considered. It is demonstrated that the normal mode spectrum in a two-dimensional rectangular lattice cannot be obtained only with inclusion of the interaction between the nearest neighbors. The discrete equations describing normal modes are derived and analyzed. The possibility of forming the anisotropic spectra of elementary excitations is investigated for different parameters of the interatomic interaction potential. It is shown that the anisotropy of the phonon spectra in two-dimensional systems can manifest itself in different kinetic effects in which the electron-phonon interaction plays the decisive role.