Dynamic localization in continuous ac electric fields

We present a detailed examination of the properties of ac electric fields that result in the dynamic localization of electrons in periodic potentials. Although exact dynamic localization can only occur if the ac electric fields are discontinuous at all changes in sign, we show that it is surprisingly tolerant to smoothing these discontinuities. We also show that within the nearest-neighbor tight-binding limit, all symmetric ac electric fields are guaranteed to exhibit dynamic localization for some field amplitude provided that the vector potential and electric field are never zero simultaneously. Finally, we derive an area theorem for symmetric electric fields with only two zeros per period.