Wannier-Stark states in double-periodic lattices I: one-dimensional   lattices
  We analyze the Wannier-Stark spectrum of a quantum particle in generic one-dimensional double-periodic lattices. In the limit of weak static field the spectrum is shown to be a superposition of two Wannier-Stark ladders originated from two Bloch subbands. As the strength of the field is increased, the spectrum rearranges itself into a single Wannier-Stark ladder. We derive analytical expressions which describe the rearrangement employing the analogy between the Wannier-Stark problem and the driven two-level system in the strong-coupling regime. 
D.N. Maksimov, E.N. Bulgakov, and A.R. Kolovsky
quant-ph