Unsteady ballistic heat transport in a 1D harmonic crystal due to a source on an isotopic defect

In the paper we apply asymptotic technique based on method of stationary phase and obtain approximate analytical description thermal motions caused by a source an isotopic defect arbitrary mass in 1D harmonic crystal. It is well known that localized oscillation possible this system case light defect. We consider unsteady heat propagation formulae, which provide continualization (everywhere excepting neighbourhood defect) uncoupling motion into sum slow fast components. The related to ballistic transport, whereas energy transformation kinetic potential one opposite direction. To propagating component estimate exact solution integral form at moving point observation. demonstrate parts are “anti-localized” near physical meaning anti-localization tendency for wave-field avoid effect increases with absolute value difference between alternated regular particle, and, therefore, more concentrates just behind leading wave-front component. obtained valid wide range spatial co-ordinate (i.e. particle number), everywhere wave-front.