Phonon green's function for polymer chains. II. a semianalytical method for the exact computation of the green's function for regular polymers

Abstract

AbstractAn exact method is presented for calculating the density of states and any complex matrix element of the harmonic phonon Green's function of single polymer chains of infinite length. The method takes advantage of the one dimensionality of the Brillouin zone. In comparison to the standard root sampling method, the method presented here has all the advantages of a fully analytic procedure (in particular, smooth curves instead of histograms) and offers and enormous increase in accuracy while at the same time drastically decreasing the computer time. For illustrational purposes, the method is applied to the defect model of Opaskar and Krimm and to the diatomic linear chain. In addition to the reproduction of the results obtained by Opaskar and Krimm, explicit expressions for the resonance and localized modes are derived.