Chaotic wave functions and ballistic transport in nonlinear superlattices

We consider superlattices built out of materials which in the bulk show strong nonlinear behavior. The nonlinear tight-binding Schr\"odinger equation, cast in the form of a discrete map, is used to describe electronic excitations in these systems. The dynamics of this map is complex and admits periodic, aperiodic, and chaotic solutions. These states affect in a nontrivial way transmission through a nonlinear material by opening infinitely many nonlinear gaps.