Response functions and classical semi-infinite linear chain

Abstract

The semi-infinite linear chain has been studied by the response function method, where the response method has been previously worked out in the semi-infinite monatomic chain by E.N.Martinez. Martinez's work has been extended and applied to the forced semi-infinite diatomic chain. Here the response function is the force-acceleration response function. The diatomic chain problem presented here has been proposed to yield two recursion relations and two coupled response functions (X1 and X2). These response functions have yielded the relationship between the displacement of the considered mass and the displacement of its nearest mass. We have, in addition, observed the energy transport in the chain by the consideration of the energy flux from these response functions. The problem of the forced semi-infinite diatomic chain which has been solved by the response function method has also been compared to the Bloch function method.