Effect of an Isotopic Impurity on the Heat Flow in One-Dimensional Coupled Harmonic Oscillators

Abstract

The effect of an isotopic impurity atom on the energy transport along the one-dimensional harmonic lattice is investigated. Assuming such an initial ensemble that the half of the system is at temperature T and the other half is at temperature zero, the mean energy of each particle is calculated as the function of time. Thus it can be shown that, for the infinitely long chain, the mean energy of each particle approaches to the different stationary values in both sides of the impurity site, namely the system finally reaches a stationary state which has a gap of the energy distribution at the impurity site. The energy flow along this linear system is also calculated.