A moment based approach to the dynamical solution of the Kuramoto model

We examine the dynamics of the Kuramoto model with a new analytical approach. By defining an appropriate set of moments the dynamical equations can be exactly closed. We discuss some applications of the formalism like the existence of an effective Hamiltonian for the dynamics. We also show how this approach can be used to numerically investigate the dynamical behavior of the model without finite size effects.Comment: 6 pages, 5 figures, Revtex file, to appear in J. Phys.

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.

Two mini-band model for self-sustained oscillations of the current through resonant tunneling semiconductor superlattices

A two miniband model for electron transport in semiconductor superlattices that includes scattering and interminiband tunnelling is proposed. The model is formulated in terms of Wigner functions in a basis spanned by Pauli matrices, includes electron-electron scattering in the Hartree approximation and modified Bhatnagar-Gross-Krook collision tems. For strong applied fields, balance equations for the electric field and the miniband populations are derived using a Chapman-Enskog perturbation technique. These equations are then solved numerically for a dc voltage biased superlattice. Results include self-sustained current oscillations due to repeated nucleation of electric field pulses at the injecting contact region and their motion towards the collector. Numerical reconstruction of the Wigner functions shows that the miniband with higher energy is empty during most of the oscillation period: it becomes populated only when the local electric field (corresponding to the passing pulse) is sufficiently large to trigger resonant tunneling.Comment: 26 pages, 3 figures, to appear in Phys. Rev.

Chapman-Enskog method and synchronization of globally coupled oscillators

The Chapman-Enskog method of kinetic theory is applied to two problems of synchronization of globally coupled phase oscillators. First, a modified Kuramoto model is obtained in the limit of small inertia from a more general model which includes ``inertial'' effects. Second, a modified Chapman-Enskog method is used to derive the amplitude equation for an O(2) Takens-Bogdanov bifurcation corresponding to the tricritical point of the Kuramoto model with a bimodal distribution of oscillator natural frequencies. This latter calculation shows that the Chapman-Enskog method is a convenient alternative to normal form calculations.Comment: 7 pages, 2-column Revtex, no figures, minor change

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

Current-voltage characteristic and stability in resonant-tunneling n-doped semiconductor superlattices

We review the occurrence of electric-field domains in doped superlattices within a discrete drift model. A complete analysis of the construction and stability of stationary field profiles having two domains is carried out. As a consequence, we can provide a simple analytical estimation for the doping density above which stable stable domains occur. This bound may be useful for the design of superlattices exhibiting self-sustained current oscillations. Furthermore we explain why stable domains occur in superlattices in contrast to the usual Gunn diode.Comment: Tex file and 3 postscript figure

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

Self-sustained spin-polarized current oscillations in multiquantum well structures

Nonlinear transport through diluted magnetic semiconductor nanostructures is investigated. We have considered a II–VI multiquantum well nanostructure whose wells are selectively doped with Mn. The response to a dc voltage bias may be either a stationary or an oscillatory current. We have studied the transition from stationary to time-dependent current as a function of the doping density and the number of quantum wells. Analysis and numerical solution of a nonlinear spin transport model shows that the current in a structure without magnetic impurities is stationary, whereas current oscillations may appear if at least one well contains magnetic impurities. For long structures having two wells with magnetic impurities, a detailed analysis of nucleation of charge dipole domains shows that self-sustained current oscillations are caused by repeated triggering of dipole domains at the magnetic wells and motion towards the collector. Depending on the location of the magnetic wells and the voltage, dipole domains may be triggered at both wells or at only one. In the latter case, the well closer to the collector may inhibit domain motion between the first and the second well inside the structure. Our study could allow design of oscillatory spin-polarized current injectors

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