Electric fields on quasiperiodic potentials

The effects of an electric field on the electronic spectrum and localization properties of quasiperiodic chains are studied. As quasiperiodic systems, we use the Harper and the Fibonacci potentials since we prove that both are closely interrelated. In the limit of a strong field, a ladder spectrum with localized states is observed. The ladder structure can be understood by using perturbation theory. Then each local isomorphism class of the quasiperiodic potential reproduces its structure in the ladder. In the case of a weak field, we observed that the singular spectrum of the quasiperiodic potential tends to be smoothed, and the gaps decrease linearly with the field. Such an effect can be understood using a variational approach, perturbation theory and a series of approximants. When the electric field and the quasiperiodic potential have the same order of magnitude, it is possible to observe a delocalization effect due to local resonances.