Quantum chaos with nonperiodic, complex orbits in the resonant tunneling diode

We show that special types of orbits, which are nonperiodic and complex "sa ddle orbits" (SOs), describe accurately the quantal and experimental curren t oscillations in the resonant tunneling diode in tilted fields. The SOs so lve the puzzle of broad regions of experimental oscillations where we find no real or complex periodic orbit (PO) that can explain the data. The SOs s ucceed in regimes involving several nonisolated POs, where PO formulas fail . We show that their contribution can, unexpectedly, decay very slowly in t he classical limit.