Delayed feedback control in quantum transport

Feedback control in quantum transport has been predicted to give rise to several interesting effects, amongst them quantum state stabilisation and the realisation of a mesoscopic Maxwell's daemon. These results were derived under the assumption that control operations on the system be affected instantaneously after the measurement of electronic jumps through it. In this contribution I describe how to include a delay between detection and control operation in the master equation theory of feedback-controlled quantum transport. I investigate the consequences of delay for the state-stabilisation and Maxwell's-daemon schemes. Furthermore, I describe how delay can be used as a tool to probe coherent oscillations of electrons within a transport system and how this formalism can be used to model finite detector bandwidth.Comment: 13 pages, 5 figure

Resonant control of stochastic spatio-temporal dynamics in a tunnel diode by multiple time delayed feedback

We study the control of noise-induced spatio-temporal current density patterns in a semiconductor nanostructure (double barrier resonant tunnelling diode) by multiple time-delayed feedback. We find much more pronounced resonant features of noise-induced oscillations compared to single time feedback, rendering the system more sensitive to variations in the delay time $\tau$. The coherence of noise-induced oscillations measured by the correlation time exhibits sharp resonances as a function of $\tau$, and can be strongly increased by optimal choices of $\tau$. Similarly, the peaks in the power spectral density are sharpened. We provide analytical insight into the control mechanism by relating the correlation times and mean frequencies of noise-induced breathing oscillations to the stability properties of the deterministic stationary current density filaments under the influence of the control loop. Moreover, we demonstrate that the use of multiple time delays enlarges the regime in which the deterministic dynamical properties of the system are not changed by delay-induced bifurcations

Controlling surface morphologies by time-delayed feedback

We propose a new method to control the roughness of a growing surface, via a time-delayed feedback scheme. As an illustration, we apply this method to the Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25,0.33], for a significant length of time. The method is quite general and can be applied to a wide range of growth phenomena. A possible experimental realization is suggested.Comment: 4 pages, 3 figure

Symmetry-breaking transitions in networks of nonlinear circuit elements

We investigate a nonlinear circuit consisting of N tunnel diodes in series, which shows close similarities to a semiconductor superlattice or to a neural network. Each tunnel diode is modeled by a three-variable FitzHugh-Nagumo-like system. The tunnel diodes are coupled globally through a load resistor. We find complex bifurcation scenarios with symmetry-breaking transitions that generate multiple fixed points off the synchronization manifold. We show that multiply degenerate zero-eigenvalue bifurcations occur, which lead to multistable current branches, and that these bifurcations are also degenerate with a Hopf bifurcation. These predicted scenarios of multiple branches and degenerate bifurcations are also found experimentally.Comment: 32 pages, 11 figures, 7 movies available as ancillary file

Strain-controlled correlation effects in self-assembled quantum dot stacks

We show that elastic interactions of an array of self-assembled quantum dots in a parent material matrix are markedly distinct from the elastic field created by a single point defect, and can explain the observed abrupt correlation--anticorrelation transition in semiconductor quantum dot stacks. Finite volume effects of the quantum dots are shown to lead to sharper transitions. Our analysis also predicts the inclination angle under which the alignment in successive quantum dot layers occurs in dependence on the material anisotropy

Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators

We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous oscillatory states of the network. Applying the speed-gradient method, we derive an adaptive algorithm for an automatic adjustment of the coupling phase such that a desired state can be selected from an otherwise multistable regime. We propose goal functions based on both the difference of the oscillators and a generalized order parameter and demonstrate that the speed-gradient method allows one to find appropriate coupling phases with which different states of synchronization, e.g., in-phase oscillation, splay or various cluster states, can be selected.Comment: 8 pages, 7 figure

A hybrid model for chaotic front dynamics: From semiconductors to water tanks

We present a general method for studying front propagation in nonlinear systems with a global constraint in the language of hybrid tank models. The method is illustrated in the case of semiconductor superlattices, where the dynamics of the electron accumulation and depletion fronts shows complex spatio-temporal patterns, including chaos. We show that this behavior may be elegantly explained by a tank model, for which analytical results on the emergence of chaos are available. In particular, for the case of three tanks the bifurcation scenario is characterized by a modified version of the one-dimensional iterated tent-map.Comment: 4 pages, 4 figure

Control of coherence resonance in semiconductor superlattices

We study the effect of time-delayed feedback control and Gaussian white noise on the spatio-temporal charge dynamics in a semiconductor superlattice. The system is prepared in a regime where the deterministic dynamics is close to a global bifurcation, namely a saddle-node bifurcation on a limit cycle ({\it SNIPER}). In the absence of control, noise can induce electron charge front motion through the entire device, and coherence resonance is observed. We show that with appropriate selection of the time-delayed feedback parameters the effect of coherence resonance can either be enhanced or destroyed, and the coherence of stochastic domain motion at low noise intensity is dramatically increased. Additionally, the purely delay-induced dynamics in the system is investigated, and a homoclinic bifurcation of a limit cycle is found.Comment: 7 pages, 7 figure