Green's Function Method in Lattice Dynamics

Abstract

This chapter discusses the application of the thermodynamic Green's function method to the study of problems in lattice dynamics. It serves two basic purposes. The first one is to discuss the motivation of the introduction of the concept of Green's function or correlation function from the physical point of view, and the second one is to present the computational technique by which significant physical quantities are calculated. The reason for choosing the topic of lattice dynamics is that it is one of the most fundamental and familiar problems in solid state physics. The Green's function method has become an invaluable tool in the study of complicated systems of interacting particles in statistical physics. The method provides a rigorous and systematic approach in extracting essential physical information. There exist a large number of publications dealing with various aspects of the Green's function method. The fundamental starting point of obtaining a theory to describe the dynamics of lattice vibrations is the total Hamiltonian of all the nuclei and electrons in the solid.