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### Nonlinear, chaotic and noise-induced front dynamics in nanostructures

Semiconductor superlattices consist of a periodic layer sequence of two different materials; they can be understood as a periodic configuration of potential barriers and quantum wells. For sufficiently large applied field a strongly nonlinear, peaked current density-field characteristic exists, due to resonant tunneling from the ground state in a quantum well to the excited state in the neighbouring well. This system exhibits very rich deterministic spatio-temporal patterns and bifurcation scenarios. For appropriate boundary conditions at the emitting contact, a charge accumulation or depletion front is generated and moves towards the collector. These fronts separate regions of high and low fields (high- and low- field domains respectively) in the form of a kink- and antikink-profile, respectively. Depending on the boundary conditions either stationary or moving fronts develop. In the stationary case the front can be - in principle - localized in each quantum well, which yields the system highly multistable. If the contact conductivity is low enough, moving fronts are generated and travel from the emitter to the collector, associated with self-sustained periodic and chaotic current oscillations. The different velocities of the accumulation adn depletion fronts depend on the number of the existing fronts in the system. Thereby, collision and anihilation of front pairs of opposite charge can occur. The chaotic front patterns consist of an irregular sequence of the position in the superlattice where the front pairs annihilate. We have generalized this spatially one-dimensional model taking into account the lateral charge distribution perpendicular to the current flow in two spatial dimensions and studied the coupled lateral and vertical charge dynamics.

A further focus was to extend the model by adding a noise term. When one choses the system parameters such that the deterministic system exhibits only stationary fronts, the global dynamics of the system changes dramatically due to the noise term and moving fronts are generated. These fronts show distinct coherence resonance. We were able to show that this behaviour reflects the signature of a global bifurcation in the corresponding deterministic spatio-temporal system: a saddle-node bifurcation on a limit cycle (saddle-node infinite period bifurcation, SNIPER). Thus, we have identified a system with excitable spatio-temporal front dynamics.

In another parameter regime, the system undergoes a Hopf bifurcation of stationary fronts. Slightly below this Hopf bifurcation, noise-induced oscillations of the fronts are observed. Through a time-delayed feedback loop we could control these noise-induced oscillations, i. e. the correlation time increases for optimal delay time, the peaks of the noisy power spectra become sharper and the dominant peak shows similar behavior in dependence on the time delay, as the purely temporal models described above.