Chaos in resonant-tunneling superlattices

Spatio-temporal chaos is predicted to occur in n-doped semiconductor superlattices with sequential resonant tunneling as their main charge transport mechanism. Under dc voltage bias, undamped time-dependent oscillations of the current (due to the motion and recycling of electric field domain walls) have been observed in recent experiments. Chaos is the result of forcing this natural oscillation by means of an appropriate external microwave signal.Comment: 3 pages, LaTex, RevTex, 3 uuencoded figures (1.2M) are available upon request from [email protected], to appear in Phys.Rev.

Chaotic motion of space charge wavefronts in semiconductors under time-independent voltage bias

A standard drift-diffusion model of space charge wave propagation in semiconductors has been studied numerically and analytically under dc voltage bias. For sufficiently long samples, appropriate contact resistivity and applied voltage - such that the sample is biased in a regime of negative differential resistance - we find chaos in the propagation of nonlinear fronts (charge monopoles of alternating sign) of electric field. The chaos is always low-dimensional, but has a complex spatial structure; this behavior can be interpreted using a finite dimensional asymptotic model in which the front (charge monopole) positions and the electrical current are the only dynamical variables.Comment: 12 pages, 8 figure

Generalized drift-diffusion model for miniband superlattices

A drift-diffusion model of miniband transport in strongly coupled superlattices is derived from the single-miniband Boltzmann-Poisson transport equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent Chapman-Enskog method to analyze the hyperbolic limit, at which collision and electric field terms dominate the other terms in the Boltzmann equation. The reduced equation is of the drift-diffusion type, but it includes additional terms, and diffusion and drift do not obey the Einstein relation except in the limit of high temperatures.Comment: 4 pages, 3 figures, double-column revtex. To appear as RC in PR

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly stablished.Comment: 10 pages, 6 Post-Script figure

Quantitative determination of modal content and morphological properties of coal sulphides by digital image analysis as a tool to check their flotation behaviour

An efficient depression of coal sulphides in the flotation process means a healthier environment and may be essential for the sustainability of a coal operation. Nitric and ferric oxidative pre-treatment of coal pyrite have been tested to improve pyrite depression, and the results are compared with those from the process of raw, not pre-treated coal. The removal indexes point to nitric pre-treatment as the best, but depression is still low. The microscopic study of feed and products, coupled to Digital Image Analysis (DIA) in all the cases, provide important clues to understand the behaviour of pyrite, which can be related to quantitative parameters, such as the exposition ratio (ER), and to qualified interpretation of the textures. Pyrite shows in the first float an unexpected hydrophobic behaviour, which is due to its occurrence as framboids, or porous particles which may be intergrown with organic matter and behave as coal. In general, the flotation results can be predicted from the DIA-data, e.g. depression of liberated pyrite into the tailings, increased by oxidative pre-treatments by 300% (ferric) or by > 400% (nitric); or concentration of middlings with lower pyrite ER in the floats. DIA is an efficient tool to obtain some important quantitative informations which otherwise would be inaccessible (e.g. the morphological data on > 1,000,000 pyrite particles for this study), and its use should be enhanced to check ore processing

On the Persson-Strang’s Identity for the Legendre Polynomials

We show an alternative proof of an identity given by Persson-Strang for the well known Legendre polynomials.&nbsp

Dynamics of Electric Field Domains and Oscillations of the Photocurrent in a Simple Superlattice Model

A discrete model is introduced to account for the time-periodic oscillations of the photocurrent in a superlattice observed by Kwok et al, in an undoped 40 period AlAs/GaAs superlattice. Basic ingredients are an effective negative differential resistance due to the sequential resonant tunneling of the photoexcited carriers through the potential barriers, and a rate equation for the holes that incorporates photogeneration and recombination. The photoexciting laser acts as a damping factor ending the oscillations when its power is large enough. The model explains: (i) the known oscillatory static I-V characteristic curve through the formation of a domain wall connecting high and low electric field domains, and (ii) the photocurrent and photoluminescence time-dependent oscillations after the domain wall is formed. In our model, they arise from the combined motion of the wall and the shift of the values of the electric field at the domains. Up to a certain value of the photoexcitation, the non-uniform field profile with two domains turns out to be metastable: after the photocurrent oscillations have ceased, the field profile slowly relaxes toward the uniform stationary solution (which is reached on a much longer time scale). Multiple stability of stationary states and hysteresis are also found. An interpretation of the oscillations in the photoluminescence spectrum is also given.Comment: 34 pages, REVTeX 3.0, 10 figures upon request, MA/UC3M/07/9

Estudio comparativo de dos métodos de radiografías forzadas para detectar la insuficiencia del ligamento cruzado anterior

En 32 pacientes con rotura unilateral de ligamento cruzado anterior (LCA) comprobada mediante artroscopia se efectuó previamente una radiografía forzada de ambas rodillas para estudiar el desplazamiento anterior de la tibia. Cada paciente fue estudiado mediante dos métodos diferentes, Lachman activo radiológico (LAR) y TelosR. Se asumió el diagnóstico radiológico de inestabilidad cuando la diferencia en el desplazamiento entre la rodilla lesionada y su control fue superior a 3 mm. Los resultados demuestran que la diferencia media del desplazamiento entre la rodilla lesionada y la normal fue superior a 3 mm con ambos métodos. En el lado interno 3,7 ± 3,7 mm con el LAR y 4,8 ± 5,8 mm con el Telos (diferencias no significativas). En el lado externo esta diferencia fue de 4,3 ± 4,7 nun con el LAR y de 6,8 ± 6 mm con el Telos (p < 0,05). A pesar de estos resultados, ambos métodos mostraron una sensibilidad para la detección de la insuficiencia ligamentosa inferior al 70%, lo que cuestiona su valor para el diagnóstico de la misma.In a prospective study, 32 patients with arthroscopically proved anterior cruciate ligament rupture were previously stressradiographied on both knees through two methods: the quadriceps-contraction technique (QCT) and the TelosR device. Instability was assumed when radiological differential displacement between injured and normal knee was greated than 3 mm. Results showed that this differential displacement was greater than 3 mm with both methods: 3,7 ± 3,7 mm v.s. 4,8 ± 5,8 mm in the medial side (differences not significant) and 4,3 ± 4,7 mm v.s. 6,8 ± 6 mm (p < 0.05) for the lateral side with the QCT and TelosR respectively. In spite of these differences, both methods showed a sensitivity lower than 70%

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

Chaotic dynamics of electric-field domains in periodically driven superlattices

Self-sustained time-dependent current oscillations under dc voltage bias have been observed in recent experiments on n-doped semiconductor superlattices with sequential resonant tunneling. The current oscillations are caused by the motion and recycling of the domain wall separating low- and high-electric- field regions of the superlattice, as the analysis of a discrete drift model shows and experimental evidence supports. Numerical simulation shows that different nonlinear dynamical regimes of the domain wall appear when an external microwave signal is superimposed on the dc bias and its driving frequency and driving amplitude vary. On the frequency - amplitude parameter plane, there are regions of entrainment and quasiperiodicity forming Arnol'd tongues. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Coexistence of up to four electric-field domains randomly nucleated in space is detected under ac+dc driving.Comment: 9 pages, LaTex, RevTex. 12 uuencoded figures (1.8M) should be requested by e-mail from the autho