Nonlinearity Effect on 1D Periodic and Disordered Lattices

The Kronig-Penney model is used to study the effect of nonlinear interaction on the transmissive properties of both ordered and disordered chains. We found that nonlinearity can either localize or delocalize the electronic states in ordered systems depending on both its sign and strength but there exists a critical strength above which all states are localized. In the disordered case, however, we found that the transmission has a power law decay at the band edge of the corresponding periodic system T ≃ L . The exponent γ seems to be independent of the strength of the disorder in the case of barrier potentials, while it seems to vary linearly with the logarithm of this strength for mixed potentials. Extensive results on the effect of nonlinearity on the nature of the eigenstates are also provided. Keyword: Band spectrum, non-linearity, interaction, disorder.