Finite lifetimes for intermediate phonon lines in anharmonic perturbation theory

Abstract

The spectral functions for a linear chain show strong singularities when calculated with the usual perturbation-theory expressions. Results from molecular-dynamics simulations show no such signularities. We modify the perturbation-theory calculation to include lifetimes, and hence widths, for the intermediate phonons in the cubic term. The widths and shifts of the intermediate lines are assumed, for simplicity, to be proportional to their frequencies, and are calculated self-consistently. The agreement with the molecular-dynamics results is substantially improved.