Dephasing of Local Vibrations in a Planar Lattice of Adsorbed Molecules

We investigate anharmonically coupled high- and low-frequency excitations in a planar lattice of adsorbed molecules interacting with phonons of a crystal. Dephasing of high-frequency local vibrations by low-frequency resonance modes is described in terms of temperature Green's function. The equations obtained are solved, first, with a small ratio of the anharmonic coupling coefficient for high- and low-frequency modes to the resonance width, and second, in the low-temperature limit. High-frequency spectral line positions and widths depend on dispersion laws and resonance mode lifetimes. It is shown that lateral interactions of low-frequency modes of adsorbed molecules can lead to a significant narrowing of high-frequency spectral lines, which is consistent with experimental data.