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Control of noise-induced spatiotemporal patterns in superlattices

We investigate a semiconductor superlattice exhibiting complex dynamics of electron accumulation and depletion fronts (travelling field domains) in the presence of noise and control. In the uncontrolled system noise is able to induce electron charge front motion through the device when the system is prepared near a global bifurcation which yields it highly sensitive to fluctuations. The associated current density oscillations exhibit a maximum of coherence at an optimal noise intensity, a phenomenon known as coherence resonance. We show how control in the form of a time-delayed feedback signal affects the noise-induced dynamics. We observe that control induces a limit cycle in a wide range of the control parameter space and therefore destroys the effect of coherence resonance. For low noise intensity, time-delayed feedback control enhances the regularity (coherence) of the noisy oscillations considerably. 1 Introduction Superlattices are well known to exhibit complex dynamic behavior if they are driven by a high dc bias into the regime of negative differential conductivity. We consider a sequential tunneling model [1], which assumes that electrons are localized in one particular well and only weakly coupled to the adjacent wells. The tunneling current density Jm→m+1(Fm ,n m ,n m+1) from well m to well m +1 depends only on the electric field Fm between both wells and the electron densities nm and nm+1 in the respective wells. We extend the deterministic model by taking into account random fluctuations of the current densities which we approximate by additive Gaussian white noise ξm(t) with � ξm(t)� =0 and � ξm(t)ξm (t � )� = δ(t − t � )δmm. We thus obtain the following Langevin equations: