Nonlocal complex Ginzburg-Landau equation for electrochemical systems

By means of an extended center-manifold reduction, we derive the nonlocal complex Ginzburg-Landau equation (NCGLE) valid for electrochemical systems with migration coupling. We carry out the stability analysis of the uniform oscillation, elucidating the role of the nonlocal coupling in electrochemical systems at the vicinity of a supercritical Hopf bifurcation. We apply the NCGLE to an experimental system, an N-type negative differential resistance electrochemical oscillator, which is shown to exhibit electrochemical turbulence for wide parameter ranges.     

High frequency amplification in quantum well oscillators

We have calculated the frequency limit of negative differential resistance and a.c. amplification of quantum well oscillators. From the time development of resonant tunneling, negative resistance is expected to occur at very high frequencies. However, the large device impedance results in a resistive cut-off frequency that is several orders of magnitude below that predicted from transit time considerations. This cut-off frequency is estimated from an equivalent circuit model, and the power of an oscillator as a function of frequency and negative resistance is found from a transmission line model.     

负微分迁移率和碰撞电离对GaAs光导开关非线性特性的影响

对GaAs光导开关非线性工作时,负微分迁移率和碰撞电离的作用进行了数值分析,给出了考虑和未考虑碰撞电离作用时的外电路电流输出波形,以及载流子和电场的空间分布和随时间演变的情况.计算表明GaAs材料的负微分迁移率引起的微分负阻,会导致阴极附近电场的动态增强,使得阴极附近的电场达到本征碰撞电离发生的阈值电场,从而引发本征碰撞电离的发生.分析结果表明,碰撞电离可以极大地延长电流输出的时间,但仅考虑负微分迁移率特性的本征碰撞电离过程不足以完全解释观察到的所有非线性现象,必须进一步考虑其它高电场效应.     

Coexisting attractors control of anomalous transport in a vibrational motor

Three anomalous transport phenomena are theoretically predicted in a vibrational motor, where an additional temporally periodic signal plays analogous role of noise in a Brownian motor. By manipulating the amplitude of the additional periodic signal, absolute negative mobility, negative nonlinear mobility and differential negative mobility are observed. The parameter regimes for the abnormal transport behaviors are identified. Coexisting attractors are responsible for these anomalous transport phenomena.     

Exact folded-band chaotic oscillator

An exactly solvable chaotic oscillator with folded-band dynamics is shown. The oscillator is a hybrid dynamical system containing a linear ordinary differential equation and a nonlinear switching condition. Bounded oscillations are provably chaotic, and successive waveform maxima yield a one-dimensional piecewise-linear return map with segments of both positive and negative slopes. Continuous-time dynamics exhibit a folded-band topology similar to Ro?ssler's oscillator. An exact solution is written as a linear convolution of a fixed basis pulse and a discrete binary sequence, from which an equivalent symbolic dynamics is obtained. The folded-band topology is shown to be dependent on the symbol grammar.     

Integrable deformations of integrable Hamiltonian systems

We give new effective necessary conditions for the integrability of nonhomogeneous potentials which are sums of two homogeneous terms. These conditions were deduced from an analysis of the differential Galois group of variational equations. We apply the obtained result to polynomial perturbations of linear oscillator with two degrees of freedom.     

非高斯噪声对惯性棘轮中粒子负迁移率的影响

利用随机模拟方法研究了惯性棘轮中非高斯噪声对负迁移率的影响. 分别模拟了绝对负迁移率(ANM), 非线性迁移率(NNM) 和负微分迁移率(NDM) 等三种反常输运现象. 计算结果表明: 1) 在不同的参数空间里, 非高斯噪声参数q 能够增强或者削弱ANM, 诱导NNM 和NDM; 2) 当q 较大时, 反常输运现象转化为正常输运; 3) 随着q 逐渐增大, 平均速度- 关联时间特性曲线朝着关联时间较小的方向移动并且其峰值逐渐减小. 关键词： 反常输运 负迁移率 非高斯噪声     

Forced periodic oscillations and the Jones polynomial

We show that forced periodic oscillations in a nonlinear damped oscillator can be classified by means of the Jones (knot) polynomial; this is done by associating to any periodic oscillation a braid. We also discuss the relation of this approach to (Lie-point) symmetry analysis of the associated differential equations.     

基于差分开关振荡器的宽带电磁脉冲辐射系统

设计了一种差分开关振荡器,能够产生中心频率300 MHz的差分衰减振荡信号,并研制了基于差分开关振荡器和螺旋天线的辐射系统。首先将相同中心频率的差分开关振荡器与单端开关振荡器对比,表明差分开关振荡器的耐压和输出电压是单端开关振荡器的两倍;然后介绍了差分开关振荡器的设计方案,对其阻抗特性和静电场分布进行了分析,仿真了其瞬态工作过程;之后根据差分开关振荡器的输出形式,研制了一种差分注入的螺旋天线,作为系统的辐射天线;最后介绍了该差分型辐射系统在不同辐射距离,不同充气气压下的实验结果,并与单端型辐射系统进行了对比。结果表明,该辐射系统能够产生中心频率300 MHz,百分比带宽约20%的高功率宽带电磁脉冲,最大辐射场强约18 kV/m,有效电势约110 kV,场强与单端型辐射系统相比近似提高了1倍。     

Transport in surface superlattices

Transport and scattering in a lateral surface superlattice are investigated. A Monte Carlo calculation of the drift velocity versus electric field, using simple sinusoidal energy bands in two dimensions, shows negative differential mobility. The negative differential mobility is the result of Bloch oscillations, as is apparent from oscillations in the velocity autocorrelation function.     

On the existence and detection of Bloch oscillations in superlattices

While many predicted superlattice behaviors depend on the presence of Bloch oscillations, the existence of such oscillations remains problematical. Here, we consider procedures by which their existence within a superlattice could be detected. We first set upper and lower bounds on the necessary fields. We then demonstrate that while a negative differential mobility is expected, no resonant peak occurs in this mobility at the Bloch frequency. However, we provide two ways of directly observing Bloch oscillations. In the first, we note the existence of structures in the dc velocity-field characteristic when an externally applied RF field has a frequency which is harmonically related to the Bloch frequency. The second approach is to measure the velocity fluctuation noise spectra, which should have a peak at the field-tunable Bloch frequency.     

一种推导文氏桥电路振荡条件的新方法

提出把文氏桥电路等效成负阻振荡器的新观点，从而利用物理概念导出了该电路的振荡条件和振荡频率公式，并将结果与传统理论进行了比较。     

2+1 Dimensional Noncommutative Dirac Oscillator and (Anti)-Jaynes-Cummings Models

We study Dirac oscillator in 2+1 dimensional noncommutative space. The model is solved exactly and the relationship with Jaynes-Cummings (JC) or anti-Jaynes-Cummings (AJC) models are investigated. We find that for a positive noncommutative parameter, there is an exact map from the 2+1 dimensional noncommutative Dirac oscillator to AJC model. However, for a negative noncommutative parameter, the noncommutative planar Dirac oscillator contains both AJC and JC terms simultaneously. Our investigation may afford a new way to study relativistic quantum mechanics models in noncommutative space by means of quantum optics method, and vice verse.     

一类海-气振子模型的微扰解

文章创建一个求解关于海-气振子模型非线性方程的渐近方法,并且基于一类海-气振子模型,借助于改进的微扰方法,首先按时滞参数进行展开,然后对两小参数的相对值分为三种情形进行讨论,最后利用微分不等式理论得到了问题解的一致有效的渐近展开式.     

Domain boundary instability in weakly coupled GaAs/AlGaAs superlattices

Self-sustained oscillations of the current with a frequency ranging from 0.7 to 3.6 MHz have been detected in weakly coupled GaAs/AlGaAs superlattice at 4.2 K. A study of the static and dynamic characteristics of the structure showed that the spontaneous oscillations arise in the local region of the superlattice, restricted by a size of the domain boundary expansion. The oscillations arise in the negative differential conductivity regions due to the periodic coupling and decoupling of subbands in adjacent quantum wells, forming the expanded domain boundary. We suggest that the spatio-temporal oscillations of the domain boundary should be considered as oscillations of an ensemble of several strongly phase-coupled oscillators. Each oscillator is a couple of two adjacent quantum wells, which operates as a single resonant tunneling diode.     

Transient chaos in smooth memristor oscillator

This paper presents a new smooth memristor oscillator, which is derived from Chua's oscillator by replacing Chua's diode with a flux-controlled memristor and a negative conductance. Novel parameters and initial conditions are dependent upon dynamical behaviours such as transient chaos and stable chaos with an intermittence period and are found in the smooth memristor oscillator. By using dynamical analysis approaches including time series, phase portraits and bifurcation diagrams, the dynamical behaviours of the proposed memristor oscillator are effectively investigated in this paper.     

Superlattice vertical transport with high-lying minibands

We examine the role of high-lying minibands in superlattice vertical transport using a nonparabolic balance-equation approach. We find that the inclusion of high-lying minibands results in a decrease of the electron temperature, a reduction of the peak drift velocity and a slow-down of the velocity-drop rate in the negative differential mobility (NDM) regime, in comparison with those predicted by a single miniband model. These effects become significant when the strength of the electric field gets close to or falls in the NDM regime.     

Microwave oscillator based on Bloch oscillations of electrons in a semiconductor superlattice

We report on a microwave oscillator based on Bloch oscillations of electrons in a semiconductor superlattice. Our GaAs/AlAs superlattice, at room temperature, was coupled electromagnetically by an antenna to a rectangular cavity resonator, and was operated at a current-voltage state of negative differential conductance. We observed generation of microwave radiation at frequencies, depending on the resonator length, between 7 and 30 GHz. Electronic tuning by several percent was possible; the ratio of linewidth to frequency was of the order of 10^?4. A radiation power up to 1 μW (at 10 GHz) was obtained, corresponding to a generator efficiency of the order of 10^?3 for the conversion of electrical power to microwave radiation.     

Stationary solution of a laser oscillator with spatial dispersion

We present an exact solution of recently proposed differential equation for the space dependence of the most probable field amplitude in laser oscillator near threshold for laser action.     

Spectrally equivalent time-dependent double wells and unstable anharmonic oscillators

We construct a time-dependent double well potential as an exact spectral equivalent to the explicitly time-dependent negative quartic oscillator with a time-dependent mass term. Defining the unstable anharmonic oscillator Hamiltonian on a contour in the lower-half complex plane, the resulting time-dependent non-Hermitian Hamiltonian is first mapped by an exact solution of the time-dependent Dyson equation to a time-dependent Hermitian Hamiltonian defined on the real axis. When unitary transformed, scaled and Fourier transformed we obtain a time-dependent double well potential bounded from below. All transformations are carried out non-perturbatively so that all Hamiltonians in this process are spectrally exactly equivalent in the sense that they have identical instantaneous energy eigenvalue spectra.