Dynamics of a Disordered Diatomic Chain

Abstract

The vibrations of a chain of diatomic molecules with glasslike disorder are examined using a perturbation theory in configuration space rather than wave-number space (i.e., a perturbed Einstein model). The frequency spectrum is found from the solution of two simultaneous polynomial equations. As a test, this theory is applied to the special case of the monatomic chain, and a comparison of the results is made with the direct numerical calculation of Dean. Good agreement is obtained.