Dynamical structure factor of the Frenkel-Kontorova model

We investigate the coherent dynamical structure factorS(q, ) of the Frenkel-Kontorova model with a continued fraction expansion. The model consists of harmonically interacting particles moving in a periodic potential. It applies to quasi-one-dimensional systems where two different periods and competing interactions are important. We study commensurability effects in the collective dynamical behaviour of the particles and their manifestation inS(q, ). Our theory gives detailed results for the inelastic scattering at high temperatures. For the quasielastic peak it predicts, among other things strong oscillations of the half-width as a function of the wave vectorq. Such a behaviour can be observed in neutron scattering experiments on superionic conductors.