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 interacti on 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 c ritical strength above which all states are localized. In the disordered ca se, however, we found that the transmission decays as T similar to L-gamma around the band edge of the corresponding periodic system. The exponent gam ma is independent of the strength of the non-linearity in the case of disor dered barrier potentials, while it varies with this strength for mixed pote ntials.