Bosons Interacting with Electrons

Abstract

A consistent consideration of transport phenomena for different types of vibrational modes in solids (the branches of phonon spectrum and the modes of electromagnetic field introduced in Secs. 6 and 3, respectively) should be based upon the formalism of second quantization. Below we introduce the density matrix for bosons and derive kinetic equations for bosonic modes in the occupation number representation. The non-diagonal components of the boson density matrix describe phase correlations. In this chapter we study the case when the interaction of bosons with electron sub-system is described by the Hamiltonian linear in the creation and annihilation operators of bosons. This important case unifies the photon-electron and phonon-electron interactions in solids. Then we consider the processes of spontaneous and stimulated emission of bosons by non-equilibrium electrons, instabilities of phonon systems, and emission of three-dimensional boson modes by two-dimensional electrons. The kinetics of interacting bosons is considered in the next chapter for phonons.