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We present an analytical study of one-dimensional semiconductor superlatticesin external electric fields, which may be time-dependent. A number of generalresults for the (quasi)energies and eigenstates are derived. An equation ofmotion for the density matrix is obtained for a two-band model, and theproperties of the solutions are analyzed. An expression for the current isobtained. Finally, Zener-tunneling in a two-band tight-binding model isconsidered. The present work gives the background and an extension of thetheoretical framework underlying our recent Letter [J. Rotvig {\it et al.},Phys. Rev. Lett. {\bf 74}, 1831 (1995)], where a set of numerical simulationswere presented.

Theory of coherent time-dependent transport in one-dimensional multiband semiconductor superlattices