Dispersion of Electromagnetic, Elastic and Diffusion Waves in Crystalline Solids

Abstract

The paper analyzes the dispersion characteristics of eigen oscillation frequencies of electromagnetic, elastic and diffusion waves. The analysis is based on the general invariant expression of the Lagrange function density in a solid subjected to the elastoplastic deformation with u(r,t) strain vector of its inner points, electromagnetic field potentials A(r,t) and φ(r,t ) , and concentration n(r,t) of diffusing substance with regard to a correlation between these parameters. Owing to the least-action principle, four linear, interconnected differential equations are obtained. Form their solution all the four frequency spectra ωi (k ) are derived, where i=1,2,3,4 and k is the wave vector. It is found that the obtained dispersions are the important part in the quantum case, if taking the interaction between the four components into consideration, when knowledge of the function ωi (k ) is required.