构造具有超混沌特性的二维离散系统

用自动生成的方式构造出一类具有超混沌特性的二维离散系统,其非线性函数由幂次不高于2的多项式组成,通过计算李氏指数来判断所选的系统是否为超混沌的。不仅得到一般形式的超混沌系统,而且还在特殊限定条件下得到了一些形式简单的超混沌系统。此外,对其中两个系统的分岔特点进行了理论分析。     

Coherent branched flow in a two-dimensional electron gas

Semiconductor nanostructures based on two-dimensional electron gases (2DEGs) could form the basis of future devices for sensing, information processing and quantum computation. Although electron transport in 2DEG nanostructures has been well studied, and many remarkable phenomena have already been discovered (for example, weak localization, quantum chaos, universal conductance fluctuations), fundamental aspects of the electron flow through these structures have so far not been clarified. However, it has recently become possible to image current directly through 2DEG devices using scanning probe microscope techniques. Here, we use such a technique to observe electron flow through a narrow constriction in a 2DEG-a quantum point contact. The images show that the electron flow from the point contact forms narrow, branching strands instead of smoothly spreading fans. Our theoretical study of this flow indicates that this branching of current flux is due to focusing of the electron paths by ripples in the background potential. The strands are decorated by interference fringes separated by half the Fermi wavelength, indicating the persistence of quantum mechanical phase coherence in the electron flow. These findings may have important implications for a better understanding of electron transport in 2DEGs and for the design of future nanostructure devices.     

二维圆环弹子球体系的量子谱分析

基于自由粒子在二维圆形无限深势阱(弹子球体系)中运动的本征值和本征函数,计算了傅里叶变换的量子谱.把傅里叶变换后的量子谱中峰的位置与其所对应的经典体系的轨道长度作对照,发现傅里叶变换的量子谱的峰位和经典轨道的长度之间存在着一一对应关系,体现了体系的量子行为和经典行为的对应性.     

Observation of spin Coulomb drag in a two-dimensional electron gas

An electron propagating through a solid carries spin angular momentum in addition to its mass and charge. Of late there has been considerable interest in developing electronic devices based on the transport of spin that offer potential advantages in dissipation, size and speed over charge-based devices. However, these advantages bring with them additional complexity. Because each electron carries a single, fixed value (- e) of charge, the electrical current carried by a gas of electrons is simply proportional to its total momentum. A fundamental consequence is that the charge current is not affected by interactions that conserve total momentum, notably collisions among the electrons themselves. In contrast, the electron's spin along a given spatial direction can take on two values, +/- [planck]/2 (conventionally upward arrow, downward arrow), so that the spin current and momentum need not be proportional. Although the transport of spin polarization is not protected by momentum conservation, it has been widely assumed that, like the charge current, spin current is unaffected by electron-electron (e-e) interactions. Here we demonstrate experimentally not only that this assumption is invalid, but also that over a broad range of temperature and electron density, the flow of spin polarization in a two-dimensional gas of electrons is controlled by the rate of e-e collisions.     

Watching hydrogen-bond dynamics in a beta-turn by transient two-dimensional infrared spectroscopy

X-ray crystallography and nuclear magnetic resonance measurements provide us with atomically resolved structures of an ever-growing number of biomolecules. These static structural snapshots are important to our understanding of biomolecular function, but real biomolecules are dynamic entities that often exploit conformational changes and transient molecular interactions to perform their tasks. Nuclear magnetic resonance methods can follow such structural changes, but only on millisecond timescales under non-equilibrium conditions. Time-resolved X-ray crystallography has recently been used to monitor the photodissociation of CO from myoglobin on a subnanosecond timescale, yet remains challenging to apply more widely. In contrast, two-dimensional infrared spectroscopy, which maps vibrational coupling between molecular groups and hence their relative positions and orientations, is now routinely used to study equilibrium processes on picosecond timescales. Here we show that the extension of this method into the non-equilibrium regime allows us to observe in real time in a short peptide the weakening of an intramolecular hydrogen bond and concomitant opening of a beta-turn. We find that the rate of this process is two orders of magnitude faster than the 'folding speed limit' established for contact formation between protein side chains.     

Influence of the amplitude ratio between two terahertz pulses on two-dimensional spectroscopy

The influence of the amplitude ratio between the two THz pulses on two-dimension THz spectroscopy （2DTS） has been studied theoretically via a classical method in which the expressions for the second-order nonlinearity were derived using perturbation approach, and the THz pulses were not treated as a delta function. Three types of nonlinear sources i.e., anharmonicity, nonlinear damping, and nonlinear coupling, are considered in a single mode system. The simulation results demonstrated that the amplitude ratio had a notable influence on the 2DTSs, and different sources have different influences. This study is promising for guiding future experiments.     

Bose-Einstein condensation of excitons in bilayer electron systems

An exciton is the particle-like entity that forms when an electron is bound to a positively charged 'hole'. An ordered electronic state in which excitons condense into a single quantum state was proposed as a theoretical possibility many years ago. We review recent studies of semiconductor bilayer systems that provide clear evidence for this phenomenon and explain why exciton condensation in the quantum Hall regime, where these experiments were performed, is as likely to occur in electron-electron bilayers as in electron-hole bilayers. In current quantum Hall excitonic condensates, disorder induces mobile vortices that flow in response to a supercurrent and limit the extremely large bilayer counterflow conductivity.     

离散重复控制系统设计的二维模型方法

针对一类线性不确定系统,提出了一种基于离散二维模型的重复控制系统设计方法,通过独立考虑重复控制系统的控制与学习行为,建立了离散重复控制系统的二维模型,构造二维状态反馈控制器,将离散重复控制系统设计问题转化为一类离散二维系统的设计问题,然后应用二维系统理论和线性矩阵不等式方法,分别获得了标称和不确定重复控制系统的稳定性条件,根据稳定性条件,通过求解线性矩阵不等式,求得重复控制器参数,最后数值仿真实例验证了本研究所提方法的有效性。     

摩擦对二维颗粒体系中临界阻塞态的影响

采用离散元法(discrete element method,DEM)对双分散圆盘颗粒体系在均匀压缩过程中的阻塞转变进行数值模拟,讨论了摩擦对临界阻塞态的影响。随着摩擦系数的增大,临界阻塞态的体积分数与平均接触数减小,其力学平均接触数与几何平均接触数的差异增大,同时各种接触类型的百分比也在发生改变。模拟结果还表明,摩擦系数为零以及无穷大的临界阻塞态是等静态堆积,临界阻塞态的体积分数随力学平均接触数呈线性增长的关系。     

层状复合体系介电谱的数值模拟

为定量研究层状复合体系介电谱,基于微元法思想,提出了数值模拟该体系介电谱的方法,即将体系内电参数非均匀分布层分割为若干个电参数均匀分布的薄层,通过求解体系的复电导而得到体系的介电谱的数值解。以层内电导率和介电常数呈线性分布的介电谱为例,研究结果表明,数值模拟结果与理论解析结果一致。浓差极化层的压力驱动膜分离体系的模拟显示,该数值模拟方法可以研究复杂电参数分布情况时体系的介电谱,并发现该体系电导的频率依存性受原料液通量变化影响显著,体系弛豫个数随着通量的增加而减少。     

构造可积非自治二维线性微分方程组的一种新方法

文中建立的定理对求可积的非自治二维线性微分方程组提出了一种新方法 .在相当弱的条件下 ,用非奇异线性变换将方程组化为具斜对角系数矩阵的新方程组 ,从而把可积性判定归结到某个变系数二阶线性微分方程的讨论 .由选取后者为已知可积形式 ,并适当选取方程组的系数函数 ,即可导出许多新的可积非自治二维线性微分方程组 .     

Optimal quantum measurement of finite-dimensional systems and coherent anti-Stokes Raman spectroscopy

Quantum measurement is a fundamental problem in quantum control theory and experiments.It can obtain unknown information of quantum systems,and can also change state of the systems inevitably.Both the outcome and back action could be used to control quantum systems.This paper presents recent research progress about optimal control of state transformation in finite-dimensional quantum systems by back action of non-selective quantum measurement,and optimal control of signal and background of CARS (coherent anti-Stokes Raman spectroscopy) by phase shaping technique.In measurement sequence control of finite-dimensional quantum systems,the necessary condition for critical points of the underlying state transformation objective is found to be a highly symmetric form as a chain of equalities,and analytical and numerical solutions in several cases are explored.In the CARS control,it is found that the maximal resonant signal and minimal background at a specific frequency can be achieved by shaping the probe pulse only while keeping pump and Stokes pulses in transform limited forms (TLFs).An arctan-type phase function is obtained for the probe pulse to simultaneously enhance the resonant signal and suppress the background.For broadband background elimination,we find that the optimal phase shaping scheme of probe pulse is quasi-time-delay while keeping the pump and Stokes pulses in TLFs.These conclusions could help design control strategies of quantum devices.     

高分辨率掌纹图像的分割

研究了高分辨率掌纹图像的分割方法问题,将均值、标准差作为标准,实现了由纹线组成的掌纹图像的前帚分割。对于手指部分的干扰,将其分为孤立的手指部分和与手掌相连的手指部分分别进行处理,利用区域生长法提取最大连通域达到去除孤立手指部分的目的;利用轮廓跟踪法比较CD、PD距离,定位与手掌相连的手指部分的位置,从而实现将其去除的目标。实验结果表明,该方法很好地实现了高分辨率掌纹图像的分割,为后续的特征提取工作奠定了基础。     

基于采样数据二维连续线性系统的混沌反控制

针对状态矩阵具有复特征值的稳定二维连续线性系统,提出了一种基于采样数据的混沌反控制方法.该方法以给定的采样周期对连续系统进行采样,由采样数据的正弦函数构造反馈控制器,使连续系统产生混沌.在每个采样周期内保持控制项不变.数值仿真结果证实了该方法的有效性.作为一种数字控制技术,该方法设计的控制律较连续控制律更易于工程实现.     

Probing bulk states of correlated electron systems by high-resolution resonance photoemission

Electron correlations are known to play an important role in determining the unusual physical properties of a variety of compounds. Such properties include high-temperature superconductivity, heavy fermion behaviour and metal-to-insulator transitions. High-resolution photoelectron spectroscopy (PES) provides a means of directly probing the electronic states (particularly those near the Fermi level) in these materials, but the short photoelectron mean free paths (< or = 5 A) associated with the low excitation energies conventionally used (< or = 120 eV) make this a surface-sensitive technique. Now that high-resolution PES is possible at much higher energies, with mean free paths as long as 15 A (ref. 6), it should become feasible to probe the bulk electronic states in these materials. Here we demonstrate the power of this technique by applying it to the cerium compounds CeRu2Si2 and CeRu2. Previous PES studies of these compounds revealed very similar spectra for the Ce 4f electronic states, yet it is expected that such states should be different owing to their differing degrees of hybridization with other valence bands. Our determination of the bulk Ce 4f electronic states of these compounds resolves these differences.     

二维Lennard-Jones系统气/液相转变的Monte Carlo模拟研究

为深入研究微小尺度系统的热力学性质和相转变机制,以粒子间通过Lennard-Jones势能作用的2维系统为模型,通过正则系综Monte Carlo模拟细致地考察了气/液相转变区的平衡态参数。沿等温线的模拟结果显示了在气/液相转变区内系统状态连续变化的特征,与固/液相转变区的状态变化趋势相同。热力学性质和系统微观行为的模拟结果都表明,模拟系统的气/液相转变具有一级相变的特征,与已知的固/液一级相变相对应;从而揭示了固/液相转变和气/液相转变机制的一致性,建立了2维Lennard-Jones系统中完整并自洽的一级相变图景。     

五阶高分辨率熵稳定算法

针对双曲守恒律方程的数值求解问题,构造一种新型的熵稳定算法.新算法空间方向采用五阶中心加权基本无振荡(CWENO)重构格式,时间方向采用四阶强稳定龙格-库塔(Runge-Kutta)方法.将新算法应用于若干一维Burgers方程和Euler方程组问题数值算例的求解.结果表明:新算法精度高,有效抑制了伪振荡的产生,与理论分析的结果一致.