Forcing of chaos in semiconductor superlattices

The chaotic behavior of high-field transport in weakly-coupled narrow-miniband GaAs/AlAs superlattices (SL) under ac + dc biases has been numerically studied within a self-consistent discrete model. It is shown that the regions of entrainment and quasiperiodicity form the Arnol'd tongues on the driving frequency–driving amplitude parameter plane. Chaos is demonstrated to appear at the boundaries of the tongues and in the regions where they overlap. Numerical simulation shows that ac driving can lead to chaos for different regimes: (i) when the electric-field domains in the SL are stable; and (ii) when they are unstable (periodically oscillating).     

超晶格电流振荡的分岔图和Poincaré映射

基于超晶格输运的分立漂移模型,数值模拟了掺杂弱耦合GaAs AlAs超晶格在外加交流偏压下电场畴的输运行为.以黄金分割比固定交流驱动频率,模拟并分析不同交流幅度下电流的准周期、锁频及混沌现象.     

Quasiperiodicity in irrational interfaces

Recent work on quasiperiodicity in irrational grain boundaries is reviewed and generalized to heterophase interfaces. The concept of local isomorphism is shown to be very important at irrational interfaces, replacing translational invariance at periodic interfaces. Symmetry related variants of irrational interfaces are enumerated and line defects separating energetically degenerate domains of irrational interfaces are characterised by products of space group operations, one from each crystal. The symmetry operations relating the variants belong to a six dimensional crystal and the variants are locally isomorphic. A framework is described for discussing the symmetries and long range order at interfaces regardless of whether they are rational or irrational.     

Directed Transport of Interacting Particle Systems: Recent Progress

Recent developments in studies of directed transport processes in interacting particle systems are retrospected. Due to the interactions among elements, the directed transport process exhibits complicated and novel cooperative dynamics. We considered various possibilities in achieving ratchet motion by breaking different symmetries of many-body systems. It is shown that the directional transport can even be induced by breaking the coupling symmetry and the spatiotemporal symmetries.     

Multiple time scale chaos in a Schmitt trigger circuit

It is known that stray radio frequency signals can produce nonlinear effects that disrupt the operation of circuits, but the mechanisms by which this disruption occurs are not well known. In this paper, an emitter coupled Schmitt trigger circuit is driven with a high-frequency signal to look for disruptive effects. As the circuit makes a transition between mode locked states (period 2 and period 3, for example), there is a region of chaos in which the largest peak in the power spectrum is in between the mode-locked frequencies, and is not related to the driving frequency by an integer multiple. This chaos resembles the chaos seen during a period adding sequence, except that it contains frequencies ranging over many orders of magnitude, from the driving frequencies on the order of megahertz, down to a few hertz. It is found that only a one-transistor circuit is necessary to produce this extremely broadband chaos, and true quasiperiodicity is not seen in this circuit. The single-transistor circuit is then simulated to confirm the frequency conversion effects.     

Broken symmetries and pattern formation in two-frequency forced faraday waves

We exploit the approximate (broken) symmetries of time translation, time reversal, and Hamiltonian structure to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Using explicit parameter symmetries we determine, for the case of two-frequency forcing, how the strength of observed three-wave interactions depends on the frequency ratio and on the relative phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.     

Tunable transport with broken space–time symmetries

Transport properties of particles and waves in spatially periodic structures that are driven by external time-dependent forces manifestly depend on the space–time symmetries of the corresponding equations of motion. A systematic analysis of these symmetries uncovers the conditions necessary for obtaining directed transport. In this work we give a unified introduction into the symmetry analysis and demonstrate its action on the motion in one-dimensional periodic, both in time and space, potentials. We further generalize the analysis to quasi-periodic drives, higher space dimensions, and quantum dynamics. Recent experimental results on the transport of cold and ultracold atomic ensembles in ac-driven optical potentials are reviewed as illustrations of theoretical considerations.     

Spin-resolved edge states transport in a normal/ferromagnetic/normal topological insulator junction: The role of interface

The spin-resolved edge states transport in a normal/ferromagnetic/normal topological insulator (TI) junction is investigated numerically. It is shown that the transport properties of the hybrid junction strongly depend on the interface shape. For the junction with two sharp interfaces, a nonzero spin conductance can be generated besides the spin-split energy windows. Moreover, the axial symmetries of the in-plane spin conductance amplitude are broken. The underlying physics is attributed to the sharp-interface-induced quantum interference effect. However, for the hybrid junction with two smooth interfaces, a non-zero spin conductance can only be achieved in the spin-split energy windows. Further, the axial symmetries of the in-plane spin conductance amplitude recover. These findings may not only benefit to further apprehend the spin-dependent edge states transport in the hybrid TI junctions but also provide some theoretical bases to the application of the topological spintronics devices.     

条形DH半导体激光器高频调制光输出的频率锁定、准周期、分岔和混沌

本文从解光场方程和载流子浓度以及光子密度速率方程的自洽解出发,研究条形DH半导体激光器高频调制下光输出的频率锁定、准周期、分岔和混沌现象。结果表明,不稳定的条形半导体激光器可能出现混沌的光输出;其通向混沌的途径是准周期到混沌。所得结果与实验符合得很好,并澄清了当前理论中的混乱之处。     

Is the negative temperature coefficient of the resistivity of the quasicrystals due to chemical disorder?

We have found that the electronic transport of the binary icosahedral (i) Cd-Yb is extremely sensitive to a minute substitution of Mg for Cd atoms; the positive temperature coefficient of the resistivity (TCR) at low temperatures seen in the binary i Cd-Yb disappears by addition of only 0.1 at. % Mg and, moreover, the TCR stays negative well up to 60 at. % Mg. Such sensitiveness of the resistivity in the very dilute Mg concentration region, which is a consequence of the long coherence length (>28 A) of the conduction electrons in the quasiperiodic lattice, has led us to an unexpected conclusion: The negative TCR in the ternary i phase is due to partial chemical disorder; i.e., it is not a consequence of the quasiperiodicity.     

Prospects of experimentally reachable beyond Standard Model physics in inverse see-saw motivated <Emphasis Type="Italic">SO</Emphasis>(10) GUT

The grand unification theories based on SO(10) gauge group have been at the centre of attraction to beyond Standard Model phenomenology. The SO(10) gauge symmetry may pass through several intermediate symmetries before breaking to Standard Model. Therefore some higher symmetries may occur at the experimentally reachable scales. This feature flourishes easily in non-supersymmetric models compared to supersymmetric ones. We find that certain breaking chains give tremendous predictions for the physics being explored at various particle physics experiments. Explanation to neutrino masses through TeV scale inverse see-saw is the driving theme of the models studied.     

Emergent rotational symmetries in disordered magnetic domain patterns

Uniaxial systems often form labyrinthine domains that exhibit short-range order but are macroscopically isotropic and would not be expected to exhibit precise symmetries. However, their underlying frustration results in a multitude of metastable configurations of comparable energy, and driving such a system externally might lead to pattern formation. We find that soft x-ray speckle diffraction patterns of the labyrinthine domains in CoPd/IrMn heterostructures reveal a diverse array of hidden rotational symmetries about the magnetization axis, thereby suggesting an unusual form of emergent order in an otherwise disordered system. These symmetries depend on applied magnetic field, magnetization history, and scattering wave vector. Maps of rotational symmetry exhibit intriguing structures that can be controlled by manipulating the applied magnetic field in concert with the exchange bias condition.     

Synchronization in a chain of nearest neighbors coupled oscillators with fixed ends

We investigate a system of coupled phase oscillators with nearest neighbors coupling in a chain with fixed ends. We find that the system synchronizes to a common value of the time-averaged frequency, which depends on the initial phases of the oscillators at the ends of the chain. This time-averaged frequency decays as the coupling strength increases. Near the transition to the frozen state, the time-averaged frequency has a power law behavior as a function of the coupling strength, with synchronized time-averaged frequency equal to zero. Associated with this power law, there is an increase in phases of each oscillator with 2pi jumps with a scaling law of the elapsed time between jumps. During the interval between the full frequency synchronization and the transition to the frozen state, the maximum Lyapunov exponent indicates quasiperiodicity. Time series analysis of the oscillators frequency shows this quasiperiodicity, as the coupling strength increases.     

失谐对开放的四能级系统无粒子数反转激光的影响

提出开放的四能级双驱动场无反转激光系统的理论模型,由电偶极和旋转波近似得到其密度矩阵方程,讨论无反转激光产生的物理机制,利用数值计算结果分析探测场和驱动场失谐对系统无反转激光增益和粒子数差的影响.     

Quasiperiodicity and chaos in the Gunn effect

A model is proposed describing the Gunn effect in GaAs. Numerical results of the model exhibit frequency locking and the transition from quasiperiodicity to chaos under an externally applied periodic electrical field.     

Directed Current Induced by an Symmetrically ac Force Coexisting with a Time-Delayed Feedback

We study the transport of overdamped Brownian particles in a symmetrically periodic potential in the presence of an asymmetrically ac driving force and a time-delayed feedback.It is found that for low frequencies,the average velocity can be negative by changing the driving amplitude,for high frequencies,there exists an optimized driving amplitude at which the average velocity takes its maximum value.Additionally,there is a threshold value of driving amplitude below which no directed transport can be obtained for high frequencies.For the large value of the delay time,the average velocity is independent of the delay time.     

A simple derivation of the stochastic eigenvalue equation in the transition from quasiperiodicity to chaos

A simple derivation of the stochastic eigenvalue equation, previously obtained by irrational decimation of functional integrals, is given to show the universal scaling behavior of external noise in the transition from quasiperiodicity to chaos in dissipative systems.     

Anion-donor coupling in (TMTSF)2X salts: symmetry considerations

A study of the geometry of the structural cavity in which the anion resides in the novel (TMTSF)₂X salts has revealed a stronger than previously realized symmetry basis for the rationalization of the contrasting crystal physics displayed by salts with anions of grossly different molecular symmetries. Moreover, the asymmetry of the anion-cavity interactions in salts with tetrahedral anions leads to the identification of a principal structural driving force for anion ordering. Finally, additional symmetry arguments suggest that salts with dipolar anions with C_2v molecular symmetry are candidates for a low-temperature ferroelectric ground state.     

Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation

Numerical studies of higher-dimensional piecewise-smooth systems have recently shown how a torus can arise from a periodic cycle through a special type of border-collision bifurcation. The present article investigates this new route to quasiperiodicity in the two-dimensional piecewise-linear normal form map. We have obtained the chart of the dynamical modes for this map and showed that border-collision bifurcations can lead to the birth of a stable closed invariant curve associated with quasiperiodic or periodic dynamics. In the parameter regions leading to the existence of an invariant closed curve, there may be transitions between an ergodic torus and a resonance torus, but the mechanism of creation for the resonance tongues is distinctly different from that observed in smooth maps. The transition from a stable focus point to a resonance torus may lead directly to a new focus of higher periodicity, e.g., a period-5 focus. This article also contains a discussion of torus destruction via a homoclinic bifurcation in the piecewise-linear normal map. Using a dc-dc converter with two-level control as an example, we report the first experimental verification of the direct transition to quasiperiodicity through a border-collision bifurcation.