Symmetric bursting of focus-focus type in the controlled Lorenz system with two time scales

By employing a special feedback controlling scheme, a hyperchaotic Lorenz system with the structure of two time scales is constructed. Two kinds of bursting phenomena, symmetric fold/fold bursting and symmetric sub-Hopf/sub-Hopf bursting, can be observed in this system. Their respective dynamical behaviors are investigated by means of slow-fast analysis. In particular, symmetric fold/fold bursting is of focus-focus type, namely, both the up-state and the down-state are stable focus, which is different from the usual fold/fold bursting; Symmetric sub-Hopf/sub-Hopf bursting is also of focus-focus type, which has not been reported in previous work. Furthermore, phase plane analysis has been introduced to explore the evolution details of the fast subsystem for symmetric sub-Hopf/sub-Hopf bursting. With the variation of the parameter, symmetric sub-Hopf/sub-Hopf bursting can evolve to symmetric chaotic bursting or even hyperchaos.     

Linearization procedure for cylindrically and axially symmetric space-times

An investigation of the vacuum Einstein gravitational field equations for cylindrically and axially symmetric space-times is presented which leads to an equivalent differential system involving a simple nonlinearity only. The case when this equivalent system is linear is analyzed in detail and two methods for generating solutions of the Einstein vacuum equations are set up. As a result, in the axially symmetric case the linearity of the equivalent system characterizes completely the Kramer-Neugebauer transforms of Papapetrou line elements. Accordingly, Weyl solutions are shown to generate exhaustively both Lewis and van Stockum solutions. Analogous results are obtained also in the cylindrically symmetric case.     

The Newtonian limit of the spherically symmetric Vlasov-Einstein system

We prove that spherically symmetric solutions of the Vlasov-Einstein system with a fixed initial value converge to the corresponding solution of the Vlasov-Poisson system if the speed of lightc is taken as a parameter and tends to infinity. The convergence is uniform on compact time intervals with convergence rate 1/c ². Thus the classical Vlasov-Poisson system appears as the Newtonian limit of the general relativistic Vlasov-Einstein system in a spherically symmetric setting.     

Effect of two asymmetries on current of a Brownian particle

A Brownian particle in an asymmetric periodic potential and subjected to an asymmetric dichotomous noise was investigated. In the frame of Fokker-Planck equation, exact expression of current of the system was derived. By means of numerical calculations, the results indicate that: (i) as the symmetry of either potential or noise is broken, a steady current will form; (ii) as the two symmetries are broken simultaneously, the current does not always appear, dependent on values of symmetric parameters of the potential and the noise; (iii) the current exhibits non-monotonic behavior as a function of symmetric parameter of the potential, while monotonic behavior as a function of symmetric parameter of the noise; (iv) in the case the potential symmetry is not broken seriously, the current is greatly influenced on by the noise symmetric parameter; (v) absolute values of the current as a function of height of potential barrier first increase then approach to saturation as the spatial potential is symmetric, while varies monotonically as the dichotomous noise is symmetric. In addition, the planes of the two symmetric parameters, which determine directions of the current, are drawn.     

Study of the electric capacitance spectra on symmetric quantum-dot pattern

We have calculated the ground-state energy of the symmetric quantum-dot pattern by the ab initio calculation method, i.e. unrestricted Hartree-Fock-Roothaan (UHFR) method based on the Gaussian basis, and studied their electric capacitance spectra, assuming each quantum dot of quantum-dot pattern to be confined in a three-dimensional spherical potential well of finite depth. For the systems in question, our results show that our method and theoretical model not only give the electric capacitance peaks similar to s-shell and p-shell atom-like quantum dot, but also show some new fine-structure of electric capacitance in the symmetric quantum-dot pattern system. This method might be a feasible tool to study few-electron problems on the symmetric quantum-dot pattern system.     

快慢Lorenz-Stenflo系统分析

通过对系统的重新标度,得到了气流旋转缓慢变化时的Lorenz-Stenflo系统;基于Routh-Hurwitz准则,分析了平衡点的稳定性问题,得到了参数平面上的分岔集,这些分岔集将参数平面划分为不同的区域,在各个不同的区域对应于系统不同的解.随着参数的变化,从平衡点分岔出不同的解.此外,展示了系统的对称簇发解和对称混沌吸引子,并用快慢分析法给出了对称簇发解的产生机理. 关键词： Lorenz-Stenflo系统 快慢分析法 分岔 对称簇发     

Bistability in a hyperchaotic system with a line equilibrium

A hyperchaotic system with an infinite line of equilibrium points is described. A criterion is proposed for quantifying the hyperchaos, and the position in the three-dimensional parameter space where the hyperchaos is largest is determined. In the vicinity of this point, different dynamics are observed including periodicity, quasi-periodicity, chaos, and hyperchaos. Under some conditions, the system has a unique bistable behavior, characterized by a symmetric pair of coexisting limit cycles that undergo period doubling, forming a symmetric pair of strange attractors that merge into a single symmetric chaotic attractor that then becomes hyperchaotic. The system was implemented as an electronic circuit whose behavior confirms the numerical predictions.     

用于圆对称光束波前变换的位相型光学系统

由两个位相型衍射光学元件构成的光学变换系统可以实现一般圆对称光束的波前变换。在只需满足菲涅耳衍射近似条件下,采用稳相法与输入输出法相结合,可以设计出具有较高精度的光学变换系统。 关键词：     

自制音叉的对称性与非对称性破坏性实验研究

文中对自制对称正型音叉与自制非对称异型音叉受力F后音叉产生的振动的现象进行了研究,用DIS声传感数字化信息系统采集振动频率,研究频率与音叉叉股长度的关系,从而对音叉叉股对称与非对称的情况进行研究。     

慢变控制下Chen系统的复杂行为及其机理

由于Chen系统的控制分析大都是基于同一时间尺度,而两时间尺度耦合问题的相关研究基本上局限于单维慢变量情形.本文探讨了基于慢时间尺度上的Duffing振子,即含有两维慢子系统控制下Chen系统的动力学演化过程.给出了诸如对称式fold/fold、对称式fold/Hopf、对称式homoclinic/homoclinic等不同形式的簇发振荡行为,并揭示了其相应的产生机制,指出慢子系统中两维慢变量的相互影响导致系统产生了类似于周期激励下的簇发行为.     

Characterizing multiparticle entanglement in symmetric N-qubit states via negativity of covariance matrices

We show that higher order intergroup covariances involving even number of qubits are necessarily positive semidefinite for N-qubit separable states, which are completely symmetric under permutations of the qubits. This identification leads to a family of sufficient conditions of inseparability based on the negativity of 2kth order intergroup covariance matrices (2k相似文献   

Higher-order solutions of a matrix AKNS system associated with a Hermitian symmetric space

In this paper, we study a matrix Ablowitz–Kaup–Newell–Segur (AKNS) system associated with a Hermitian symmetric space as a follow-up study of an earlier paper. A multi-fold generalized Darboux transformation of the matrix AKNS system associated with a Hermitian symmetric space is constructed by means of determinants. Subsequently, we derive various higher-order solutions for this system, including fan-shaped rogue wave and (truncated) Kuznetsov–Ma breather solutions. Specifically, we show the fusion and fission processes for two truncated Kuznetsov–Ma breathers by taking different free parameters.     

Classification of Plane Symmetric Static Space-Times According to Their Noether Symmetries

In this paper we give a classification of plane symmetric static space-times using symmetry method. For this purpose we consider the Lagrangian corresponding to the general plane symmetric static metric in the Noether symmetry equation. This provides a system of determining equations. Solutions of this system give us classification of the plane symmetric static space-times according to their Noether symmetries. During this classification we recover all the results listed in Feroze et al. (J. Math. Phys. 42:4947, 2001) and Bashir and Ehsan (Il Nuovo Cimento B 123:1, 2008).     

纠缠相干态光场驱动下∧-型三能级原子的辐射谱

采用时间演化算符方法,研究∧-型=三能级原子与纠缠相干态光场共振相互作用的辐射谱.给出了辐射谱一般公式,并讨论在纠缠相干态光场驱动下的辐射频谱结构.结果表明,无论下能级简并与否纠缠相干态光场平均光子数很小时均出现拉比分裂,且强度随双模光场纠缠程度的增加而增加.当两下能级简并时,若两模场的平均光子数较小,辐射谱呈现对称多峰结构,若两模场的平均光子数较大,辐射谱呈现对称五峰结构.当两下能级非简并时,若两模场的平均光子数较小,辐射谱呈现对称多峰结构.若两模场的平均光子数较大,辐射谱呈现对称十峰结构.纠缠相干光与非纠缠相干光辐射谱的本质差别有两点:一是双模光场强量子关联导致纠缠度越强拉比峰强度越高;二是存在纠缠时由于两模场相干性导致辐射谱呈现对称多峰结构.     

Dynamics of Condensation in the Totally Asymmetric Inclusion Process

We study the dynamics of condensation of the inclusion process on a one-dimensional periodic lattice in the thermodynamic limit, generalising recent results on finite lattices for symmetric dynamics. Our main focus is on totally asymmetric dynamics which have not been studied before, and which we also compare to exact solutions for symmetric systems. We identify all relevant dynamical regimes and corresponding time scales as a function of the system size, including a coarsening regime where clusters move on the lattice and exchange particles, leading to a growing average cluster size. The second moment of the occupation numbers is a suitable observable to characterise the transition, and exhibits a power law scaling in this regime before saturating to stationarity following an exponential decay depending on the system size. Our results are based on heuristic derivations and exact computations for symmetric systems, and are supported by detailed simulation data.     

Implementing of Quantum Cloning with Spatially Separated Quantum Dot Spins

We propose some schemes for implementing optimal symmetric (asymmetric) 1 → 2 universal quantum cloning, optimal symmetric (asymmetric) 1 → 2 phase-covariant cloning, optimal symmetric 1 → 3 economical phase-covariant cloning and optimal symmetric 1 → 3 economical real state cloning with spatially separated quantum dot spins by choosing the single-qubit rotation angles appropriately. The decoherences of the spontaneous emission of QDs, cavity decay and fiber loss are suppressed since the effective long-distance off-resonant interaction between two distant QDs is mediated by the vacuum fields of the fiber and cavity, and during the whole process no system is excited.     

Symmetries and exact solutions of discrete nonconservative systems

Based on the property of the discrete model entirely inheriting the symmetry of the continuous system,we present a method to construct exact solutions with continuous groups of transformations in discrete nonconservative systems.The Noether's identity of the discrete nonconservative system is obtained.The symmetric discrete Lagrangian and symmetric discrete nonconservative forces are defined for the system.Generalized quasi-extremal equations of discrete nonconservative systems are presented.Discrete conserved quantities are derived with symmetries associated with the continuous system.We have also found that the existence of the one-parameter symmetry group provides a reduction to a conserved quantity;but the existence of a two-parameter symmetry group makes it possible to obtain an exact solution for a discrete nonconservative system.Several examples are discussed to illustrate these results.     

Current-driven excitations in symmetric magnetic nanopillars

We study experimentally the current-driven magnetic excitations in symmetric Co/Cu/Co nanopillars. In contrast with all the previous observations where the current of only one polarity is capable of exciting a multilayer system saturated by an externally applied magnetic field, we observe that both polarities of the applied current trigger excitations in a symmetric multilayer. This may indicate that in symmetric structures the current propels high-frequency magnetic oscillations in all magnetic layers. We argue, however, that only one layer is excited in our multilayers but, interestingly, currents of opposite polarities excite different layers. This hypothesis is supported by modeling the spin accumulation in symmetric magnetic multilayers.     

Singular Characteristics of Optical Thue–Morse Multilayers Composed of PT‐Symmetric Elements

Aperiodic 1D Thue–Morse (TM) multilayer optical structures composed of two parity‐time‐symmetric (PT‐symmetric) elements are constructed. The transfer matrix and scattering matrix are utilized for singular propagation characteristic analysis of the structures. The structures display interesting and singular properties, including an unusual eigenvalue spectra, transparency, and unidirectional reflectionless and unidirectional invisibility. Additionally, even‐generation and odd‐generation structures show a significant difference in the aforementioned four properties. The main reason for this is the symmetry difference between the two structures: for even‐generation structures, each individual element as well as the entire system with respect to the PT‐symmetry; while for the odd‐generation structures, each individual element has PT‐symmetry; however, the system as a whole does not have PT‐symmetry. The propagation characteristics of the entire structure, which is not a PT‐symmetric system being composed of PT‐symmetric elements, have not yet been reported. This work can contribute to the understanding of the TM sequence, as well as contribute to understanding the influence of the degree of PT‐symmetry on the singular optical propagation characteristics of aperiodic optical structures. Additionally, this may open new possibilities for important applications, such as the design of a diverse family of all‐optical devices with intriguing behaviors.     

面对称光学系统的初级波像差理论研究

非旋转轴对称光学系统波像差理论的建立有利于理解旋转 轴对称光学系统的装调误差和离轴三反射光学系统等非旋转轴对称光学系统的选型设计. 本文利用旋转轴对称球面光学系统的全口径初级波像差理论推导了子孔径面对称光学系统的初级波像差分布公式, 证明了面对称光学系统中的节点像差理论, 即除球差外的所有初级像差的零值节点偏离视场中心, 而不再是视场的旋转对称函数; 并首次阐述了多零值节点初级非对称像差产生的根源和变化特性. 该理论可以有效指导非对称光学系统初始结构的选择和优化设计过程. 关键词： 面对称 像差 几何光学