LINEAR ALTERNATIVE TO THE BOLTZMANN-EQUATION WITHOUT LINEARIZATION .1. ELECTRON-PHONON SCATTERING

A new form of projector is suggested leading to Time-Convolutionless Generalized Master Equations (TCL-GME) for the single-electron density matrix or the Wigner distribution function. Novel feature in the formalism is that arbitrary finite concentration of electrons is admitted. In the second order in the scattering strength and after a short period of forgetting details of initial conditions, the resulting TCL-GME turns to a linear equation with time-independent coefficients. It becomes thus an alternative to the famous Boltzmann-Uehling-Uhlenbeck equation for description of kinetic processes in solids. In contrast to the latter, however, our TCL-GME is linear even though no linearization procedure was involved.