Zener transitions and energy dissipation in small driven systems

Abstract
We consider the dynamics of an electron in a finite one-dimensional system, subject to a uniform electric field (or an electron in a ring; subject to an emf induced by a time-dependent magnetic flux). In the presence of elastic scattering due to localized potentials the driving source does not supply energy to the system in the steady state. The dissipation in the presence of inelastic scattering is evaluated. The Ohmic resistance of the system depends crucially on the inelastic rate even in the weak-localization limit.