Bloch Oscillators: motion of wave-packets

Abstract

In this paper we review some known results on the motion of Bloch Oscillators in the crystal momentum representation. We emphasize that the acceleration theorem, as usually stated by most of the authors, is incomplete, but in the case of pure Bloch states. In fact, the exact version of the acceleration theorem should contain a phase factor depending on both the time and crystal momentum variables. As we show this phase factor plays an essential role in order to understand the motion of Bloch Oscillators in the position variable.