Multi-Channel Kinetics

Abstract

The transitions of electrons, or other quasiparticles, between the states belonging to different branches of energy spectrum are often met in transport theory and can be described with the use of coupled kinetic equations for the distribution functions of these quasiparticles. There are, however, the cases when this approach is not valid, because the branches of energy spectrum are close to each other, and the consideration of non-diagonal (with respect to the branch index) components of the density matrix becomes essential. The formalism which adequately describes such cases is based upon matrix kinetic equations. In this chapter we study two examples of this kind: the electrons in different spin states coupled by spin-orbit interaction, and a pair of two-dimensional electron layers weakly coupled by tunneling. We also consider other important examples of multi-channel transport: the relaxation of electrons due to the interband transitions caused by electron-electron interaction (Auger processes) and the anomalies of electrical conductivity due to spin-dependent scattering of electrons by localized states of magnetic impurities (Kondo effect). The description of these processes is based upon a detailed consideration of the multi-channel scattering.