Electron-Impurity System

Abstract

Non-equilibrium states of the systems weakly coupled to a thermostat are well investigated because these systems are easily driven from equilibrium by relatively weak external fields. On the other hand, weakly coupled systems are usually described by means of kinetic equations, and this approach is developed below and in Chapters 4–7. In this chapter, the kinetic equation is derived and analyzed for the simplest case of electrons in a weak potential of static inhomogeneities of the crystal, for example, the impurity potential. A discussion of the approximations used below is not presented in detail because this subject is widely covered in the literature. The main features of the kinetic phenomena in solids are concerned with the complex nature of quasiparticle dynamics and interactions. For this reason, the standard results obtained for plasma have a limited applicability in solids. The quantum kinetic equation is obtained below in the operator form, which is more convenient for the cases under consideration. Such an approach allows one to formulate the kinetic equation in the most general way so that in each concrete case one has just to choose a proper representation for calculation of the matrix elements of the density matrix. Of course, one has to analyze the validity conditions for the approach of kinetic equation in each concrete case.