R. M. Rubinger

Mutual Information Rate and Bounds for It

The amount of information exchanged per unit of time between two nodes in a dynamical network or between two data sets is a powerful concept for analysing complex systems. This quantity, known as the mutual information rate (MIR), is calculated from the mutual information, which is rigorously defined only for random systems. Moreover, the definition of mutual information is based on probabilities of significant events. This work offers a simple alternative way to calculate the MIR in dynamical (deterministic) networks or between two time series (not fully deterministic), and to calculate its upper and lower bounds without having to calculate probabilities, but rather in terms of well known and well defined quantities in dynamical systems. As possible applications of our bounds, we study the relationship between synchronisation and the exchange of information in a system of two coupled maps and in experimental networks of coupled oscillators.

High-resolution parameter space of an experimental chaotic circuit.

A high-resolution codimension-two parameter space showing the abundance of complex periodic structures of an experimental chaotic circuit is reported. Such resolution was propitiated by the use of a 0.5 mV step dc voltage source as one of the control parameters. Those complex periodic structures organize themselves in a period-adding bifurcation cascade that accumulates in a chaotic region. Numerical investigations on the dynamical model were also carried out to corroborate several new features observed in the experimental high-resolution parameter space.

Temperature-dependent activation energy and variable range hopping in semi-insulating GaAs

We measured resistivity in the range of 30–390 K on four semi-insulating low-temperature grown molecular-beam epitaxy GaAs samples. The growth temperature range was from 215 °C to 315 °C. Arrhenius fittings with T−1 and hopping fitting with T−1/4 do not permit us the definition of the temperature ranges controlled by band and hopping conduction, respectively. This leads to major errors in the calculation of both activation energies and hopping parameters. We have used the differential activation energy in order to clearly identify the temperature range for the different transport mechanisms. Hopping dominates at low temperatures and band conduction at high temperatures. In-between, a mixed conduction regime is observed. We introduce a criterion to clearly define the temperature range of hopping, band and mixed conduction. The lower temperature at which mixed conduction is identified decreases for samples with increasing growth temperature. Only the sample grown at 215 °C presents both forms of hopping conduction before entering the mixed conduction regime. Hopping parameters were obtained from the fittings of the differential activation energy and the values are in good agreement with the usual method of calculating them if the correct temperature range is used.

Lyapunov exponent diagrams of a 4-dimensional Chua system

We report numerical results on the existence of periodic structures embedded in chaotic and hyperchaotic regions on the Lyapunov exponent diagrams of a 4-dimensional Chua system. The model was obtained from the 3-dimensional Chua system by the introduction of a feedback controller. Both the largest and the second largest Lyapunov exponents were considered in our colorful Lyapunov exponent diagrams, and allowed us to characterize periodic structures and regions of chaos and hyperchaos. The shrimp-shaped periodic structures appear to be malformed on some of Lyapunov exponent diagrams, and they present two different bifurcation scenarios to chaos when passing the boundaries of itself, namely via period-doubling and crisis. Hyperchaos-chaos transition can also be observed on the Lyapunov exponent diagrams for the second largest exponent.

Field-enhanced trapping in deep levels by multiple phonon emission in semi-insulating GaAs

We have carried out the time, temperature, and illumination dependencies of the current density in a semi-insulating GaAs sample grown at 300 °C under strong electric field. Standard ohmic behavior was observed at room temperature. A negative differential behavior as a function of the applied electric field was observed by lowering the temperature and increasing the photon flux, and this phenomenon was associated to the field-enhanced trapping effect. We have fit our data with a model for enhanced capture by a multiple-phonon emission capture process assisted by the applied electrical field.

Variable range hopping conduction in low-temperature molecular beam epitaxy GaAs

Electric transport properties measured by Van der Pauw resistivity experiments of Low-Temperature Molecular Beam Epitaxy (LT-MBE) GaAs samples are used to identify a method to improve the resistivity of GaAs material. We present results on five samples grown at 265, 310, 315, 325, and 345 oC. The electric measurements were carried out at temperatures ranging from 130 to 300 K. In this temperature range the dominant transport process is identified as variable range hopping. The hopping parameter plotted against the growth temperature is shown to present a maximum. The mechanisms responsible for this behavior are discussed in relation to the compensation ratio.

Impact ionization and field-enhanced trapping: Fitting current density curves for semi-insulating GaAs

Semi-insulating GaAs samples present N-shaped negative differential conductivity under high-electric fields. This behavior can be associated with two physical processes: Impact ionization (generation) and field-enhanced trapping (recombination), both of which involve trapped and free electrons. We have analyzed the j(E) characteristic curves of a GaAs sample rich in As antisite defects at different conditions of temperature and illumination. The fitting was carried out using an analytical expression for j(E) based on the competition between the above-mentioned processes. Our analysis permits us to identify the temperature and illumination ranges in which those processes are relevant. The best fittings were obtained for measurements between 150 and 200 K and using an infrared photon flux of the order of 1011 photons/cm2 s.

Low frequency oscillations in semi-insulating GaAs: A nonlinear analysis

We have observed low frequency current oscillations in a semi-insulating GaAs sample grown by low temperature molecular beam epitaxy. For this, an experimental setup proper to measure high impedance samples with small external noise was developed. Spontaneous oscillations in the current were observed for some bias conditions. Although measurements were carried out from room temperature down to liquid helium, the dynamical analysis was carried out around 200 K where the signal to noise ratio was fairly favorable. To increase the data quality we have also used a noise reduction algorithm suitably developed for nonlinear systems. We observed attractors having low embedding dimension, limit cycle bifurcations, and chaotic behavior characteristic of nonlinear dynamical processes in route to chaos. Attractor reconstruction, Poincare sections, Lyapunov exponents, and correlation dimension were also analyzed.

Parameter space of experimental chaotic circuits with high-precision control parameters

We report high-resolution measurements that experimentally confirm a spiral cascade structure and a scaling relationship of shrimps in the Chuas circuit. Circuits constructed using this component allow for a comprehensive characterization of the circuit behaviors through high resolution parameter spaces. To illustrate the power of our technological development for the creation and the study of chaotic circuits, we constructed a Chua circuit and study its high resolution parameter space. The reliability and stability of the designed component allowed us to obtain data for long periods of time (∼21 weeks), a data set from which an accurate estimation of Lyapunov exponents for the circuit characterization was possible. Moreover, this data, rigorously characterized by the Lyapunov exponents, allows us to reassure experimentally that the shrimps, stable islands embedded in a domain of chaos in the parameter spaces, can be observed in the laboratory. Finally, we confirm that their sizes decay exponentially with the period of the attractor, a result expected to be found in maps of the quadratic family.

The EL2-like metastable defect and the n- to p-type transition in silicon planar-doped GaAs

Through photo-Hall measurements at temperatures below about 120 K, we have observed the presence of a deep donor defect, with characteristics similar to those of the EL2 center, in planar-doped GaAs samples grown by molecular beam epitaxy at 300 °C. We have shown that this EL2-like center can account for the remarkable photoreleasing of electrons and holes into the conduction and valence bands, respectively. The two different kinds of carriers accumulate in two spatially separated channels, which can secondarily account for the n- to p-type transition we have observed.