Absence of localization in energy space of a Bloch electron driven by a constant electric force

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Abstract
Analytical results for the behavior of a Bloch electron driven by a constant electric force are obtained. By analyzing the propagating front of the probability for the Bloch electron to be in the uppermost reachable band at a given time, we find that there is no localization in energy space for any potential except for the Dirac comb, which is the extreme case. In analogy with the analysis in nonlinear dynamics of the connection of the long-time behavior to the quasienergy spectrum, we find that under the resonance condition there is no localization in energy space even for the Dirac comb.

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