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

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