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

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

On stochastic switching of bistable resonant-tunneling structures via nucleation

We estimate the critical size of the initial nucleus of the low current state in a bistable resonant tunneling structure which is needed for this nucleus to develop into a lateral switching front. Using the results obtained for deterministic switching fronts, we argue that for realistic structural parameters the critical nucleus has macroscopic dimensions and therefore is too large to be created by stochastic electron noise.Comment: the extended version of the Comment on "Lifetime of metastable states in resonant-tunneling structures" to appear in Phys. Rev.

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

Lateral current density fronts in asymmetric double-barrier resonant-tunneling structures

We present a theoretical analysis and numerical simulations of lateral current density fronts in bistable resonant-tunneling diodes with Z-shaped current-voltage characteristics. The bistability is due to the charge accumulation in the quantum well of the double-barrier structure. We focus on asymmetric structures in the regime of sequential incoherent tunneling and study the dependence of the bistability range, the front velocity and the front width on the structure parameters. We propose a sectional design of a structure that is suitable for experimental observation of front propagation and discuss potential problems of such measurements in view of our theoretical findings. We point out the possibility to use sectional resonant-tunneling structures as controllable three-terminal switches.Comment: to appear in J.Appl.Phy

Excitation of solitons in hexagonal lattices and ways of controlling electron transport

This is a post-peer-review, pre-copyedit version of an article published in Philosophical Transactions A: Mathematical, Physical and Engineering Sciences. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40435-017-0383-x.We construct metastable long-living hexagonal lattices with appropriately modified Morse interactions and show that highly-energetic solitons may be excited moving along crystallographic axes. Studying the propagation, their dynamic changes and the relaxation processes it appears that lump solitons create in the lattice running local compressions. Based on the tight-binding model we investigate the possibility that electrons are trapped and guided by the electric polarization field of the compression field of one soliton or two solitons with crossing pathways. We show that electrons may jump from a bound state with the first soliton to a bound state with a second soliton and changing accordingly the direction of their path. We discuss the possibility to control by this method the path of an excess electron from a source at a boundary to a selected drain at another chosen boundary by following straight pathways on crystallographic axes.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Core hole-electron correlation in coherently coupled molecules

We study the core hole-electron correlation in coherently coupled molecules by energy dispersive near edge X-ray absorption fine-structure spectroscopy. In a transient phase, which exists during the transition between two bulk arrangements, 1,4,5,8-naphthalene-tetracarboxylicacid-dianhydride multilayer films exhibit peculiar changes of the line shape and energy position of the X-ray absorption signal at the C K-edge with respect to the bulk and gas phase spectra. By a comparison to a theoretical model based on a coupling of transition dipoles, which is established for optical absorption, we demonstrate that the observed spectroscopic differences can be explained by an intermolecular delocalized core hole-electron pair. By applying this model we can furthermore quantify the coherence length of the delocalized core-exciton.Comment: 5 pages, 3 figures, Accepted Version, PRL, minor wording change

Control of unstable steady states by extended time-delayed feedback

Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This system represents a generic model of an unstable steady state which can be found for instance in a Hopf bifurcation. In addition to the original controller design, we investigate effects of control loop latency and a bandpass filter on the domain of control. Furthermore, we consider coupling of the control force to the system via a rotational coupling matrix parametrized by a variable phase. We present an analysis of the domain of control and support our results by numerical calculations.Comment: 11 pages, 16 figure

Adaptive Tuning of Feedback Gain in Time-Delayed Feedback Control

We demonstrate that time-delayed feedback control can be improved by adaptively tuning the feedback gain. This adaptive controller is applied to the stabilization of an unstable fixed point and an unstable periodic orbit embedded in a chaotic attractor. The adaptation algorithm is constructed using the speed-gradient method of control theory. Our computer simulations show that the adaptation algorithm can find an appropriate value of the feedback gain for single and multiple delays. Furthermore, we show that our method is robust to noise and different initial conditions.Comment: 7 pages, 6 figure