The effect of non-linearity on one-dimensional periodic and disordered lattices

The Kronig-Penney model is used to study the effect of non-linear interaction on the transmissive properties of both ordered and disordered chains. In the ordered case, the non-linearity can either localize or delocalize the electronic states depending on both its sign and strength, but there is a critical strength above which all states are localized. In the disordered case, however, we found that the transmission decays as T ∼ L^-γ around the band edge of the corresponding periodic system. The exponent γ is independent of the strength of the non-linearity in the case of disordered barrier potentials, while it varies with this strength for mixed potentials.