Quantum dynamics of phonon assisted emission of carriers at deep level centers

A formalism is proposed to investigate quantum dynamics of localized states involving highly non-adiabatic time-evolution of electron-lattice systems. The effect of electron itinerancy is projected onto the dynamics of local variables through an integral kernel of Volterra's integral equation. The method is applied to the problem of thermal emission of carriers at deep level centers in semiconductors. It is shown that the real situation is in the adiabatic limit, and the probability of thermal emission of the trapped carriers is one per a single lattice oscillation, if the amplitude of the oscillation exceeds a critical value but zero if not.