Coupled chains in electric and magnetic fields revisited

Coupled chains in electric and magnetic fields are discussed in terms of interplays between periodicity conditions and the factorization of the wavefunction in the wavenumber representation. Proceeding in this manner yields a quickly tractable matching condition providing the quantization rule to the alternative derivation of complex energy bands. Besides achieving a deeper understanding of Wannier–Stark ladders in terms of complex resonance energies, we now have the opportunity to establish related energy levels by resorting to a suitable conversion technique. This amounts to perform an immediate integration of such energy bands over the Brillouin-zone. Such energy levels exhibit, this time, a safe dependence on the chain parameter. Dynamic localization effects, conserved currents and stripe conductivity formulae have also been discussed.