Quantum and semiclassical inelastic electron transport

Quantum-mechanical calculation of coherent electron transmission in the presence of inelastic electron-phonon interaction is calculated and compared with the semiclassical predictions of simple first-order perturbation theory. It is found that a small electron-phonon matrix element cannot be used to justify semiclassical behavior. Only if the transmission coefficient is small enough at the phonon threshold, causing unitary feedback effects to occur primarily in reflection, do nonperturbative and first-order perturbative solutions appear qualitatively similar. There are situations in which predictions of simple perturbation theory cannot approach the nonperturbative quantum calculation even in the presence of both weak coupling and large elastic-scattering strengths.