Eletric field induced localization and nonperturbative response of a one-dimensional one-band conductor

We consider the nonperturbative nonstationary response of a one dimensional conductor and the carrier localization induced by an external electric field within the one-electron one-band tight-binding approximation in the absence of relaxation. Exact general analytic expressions for the polarization, electric current, and carrier mean square displacement are obtained. We find a new effect of absence of induced polarization in an arbitrary electric field for an electron, initially localized on one site. If the electron wavevector change Δk during one period of the field is a multiple of 2π, the electron is typically delocalized except for the localization in Bloch states at the extremums of the band and the generalized dynamic localization. If Δk/2π is noninteger, the electron is localized.