The interaction of kinks and elastic waves

Abstract

A kink on a dislocation in an isotropic elastic medium is treated as a 'point defect’ with a certain mass, constrained to move along a line and subject to a radiation reaction. A value for the mass is obtained from the well know n stretched-string model, and the radiation reaction is found by calculating the rate at which an oscillating kink radiates energy into the medium . It is found that the kink has a scattering cross-section for elastic waves which i§ proportional to the square of its width. For long waves the cross-section is independent of frequency, in contrast to the case of ordinary point defects. A kink moving through an isotropic flux of elastic waves experiences a retarding force proportional to the product of its velocity and the energy density of the waves. In connexion with a similar result for the retarding force on a dislocation moving rigidly it has been suggested that the expression for the energy density should include the zero-point energy. A formal quantum -mechanical calculation shows that this is not so in the case of a kink.