Measures of imaginarity and quantum state order

Complex numbers are widely used in classical and quantum physics.Further,they play an important role in describing quantum systems and their dynamical behaviors.Herein,we propose several measures of the imaginarity of quantum states based on l1 norm and convex functions in the framework of resource theory.Further,we investigate the quantum state order after a quantum system passes through a real channel.Rigorous proof shows that these proposed measures possess all the desirable properties for a measure of imaginarity.The connection between the measure of imaginarity based on the l1 norm and the measure of imaginarity based on relative entropy is derived.Moreover,we demonstrate that the l1 norm-based and the relative entropy-based measures of imaginarity are of the same order for qubit quantum states.Further we discuss the influences of the bit flip channel,phase damping channel,and amplitude flip channel on single qubit state order.

Sufficient Conditions of the Same State Order Induced by Coherence

In this paper, we study coherence-induced state ordering with Tsallis relative entropy of coherence, relative entropy of coherence and l1 norm of coherence, and give the sufficient conditions of the same state order induced by above coherence measures. First, we show that the above measures give the same ordering for single-qubit states in some special cases. Second, we consider some special states in a d-dimensional quantum system. We show that the above measures generate the same ordering for these special states. Finally, we discuss dynamics of coherence-induced state ordering under Markovian channels. We find amplitude damping channel changes the coherence-induced ordering even though for single-qubit states with fixed mixedness.

Dynamics of coherence-induced state ordering under Markovian channels

We study the dynamics of coherence-induced state ordering under incoherent channels, particularly four specific Markovian channels： amplitude damping channel, phase damping channel, depolarizing channel and bit flit channel for single-qnbit states. We show that the amplitude damping channel, phase damping channel, and depolarizing channel do not change the coherence-induced state ordering by l1 norm of coherence, relative entropy of coherence, geometric measure of coherence, and Tsallis relative α-entropies, while the bit flit channel does change for some special cases.

Reduced-order Kalman filtering for state constrained linear systems

This paper aims at solving the state filtering problem for linear systems with state constraints. Three classes of typical state constraints, i.e., linear equality, quadratic equality and inequality, are discussed. By using the linear relationships among different state variables, a reduced-order Kalman filter is derived for the system with linear equality constraints. Afterwards, such a solution is applied to the cases of the quadratic equality constraint and inequality constraints and the two constrained state filtering problems are transformed into two relative constrained optimization problems. Then they are solved by the Lagrangian multiplier and linear matrix inequality techniques, respectively. Finally, two simple tracking examples are provided to illustrate the effectiveness of the reduced-order filters.

Effects of notches on the order of flux-closure state formation in bi-rings by micromagnetic simulation

The effects of the number and the location of notches on the formation of flux-closure states in bi-rings with fields applied in the x direction （i.e., along the short axis direction of hi-rings） and y direction （i.e., along the long axis direction of bi-rings） are investigated using micromagnetic simulation. For the bi-rings with one notch and the bi-rings with two notches symmetric about y axis, the order of flux-closure state formation in each ring can be controlled. But the flux-closure state forms simultaneously in each ring for the bi-rings with two notches symmetric about x axis. For the bi-rings with two notches that are symmetric neither about x axis nor about y axis, only one ring can form a flux- closure state in the y-direction field and no fluxclosure state can be found in rings in the x-direction field. Therefore, logic states can be defined by controlling the order of flux-closure state formation, which can be utilized in future logic devices.

Third-order polynomial model for analyzing stickup state laminated structure in flexible electronics

Laminated hard-soft integrated structures play a significant role in the fabrication and development of flexible electronics devices. Flexible electronics have advantageous characteristics such as soft and light-weight, can be folded,twisted, flipped inside-out, or be pasted onto other surfaces of arbitrary shapes. In this paper, an analytical model is presented to study the mechanics of laminated hard-soft structures in flexible electronics under a stickup state. Thirdorder polynomials are used to describe the displacement field,and the principle of virtual work is adopted to derive the governing equations and boundary conditions. The normal strain and the shear stress along the thickness direction in the bimaterial region are obtained analytically, which agree well with the results from finite element analysis. The analytical model can be used to analyze stickup state laminated structures, and can serve as a valuable reference for the failure prediction and optimal design of flexible electronics in the future.

Higher-Order Fluctuations and Measured Phase Operators in the Squeezed Thermal States

We study the higher order fluctuations and squeezing of quadrature operators in the squeezed thermal states. In terms of measured phase operators, we discuss the fluctuations and squeezing of phases in these states. We conclude that the condition of higher order squeezing for quadrature components of the field is order independent and the fluctuations of measured phase operators are temperature independent.

Adaptive State-feedback Stabilization for More General High-order Stochastic Nonlinear Systems

适应州反馈的稳定为在的高顺序的随机的非线性的系统的一个类被调查函数 fi 的上面的界限(?? 铄吗？？

A specific state variable for a class of 3D continuous fractional-order chaotic systems

A specific state variable in a class of 3D continuous fractional-order chaotic systems is presented. All state variables of fractional-order chaotic systems of this class can be obtained via a specific state variable and its （q-order and 2q-order） time derivatives. This idea is demonstrated by using several well-known fractional-order chaotic systems. Finally, a synchronization scheme is investigated for this fractional-order chaotic system via a specific state variable and its （q-order and 2q-order） time derivatives. Some examples are used to illustrate the effectiveness of the proposed synchronization method.

Robust fault detection in linear systemsbased on full-order state observers

A parametric approach to robust fault detection in linear systems with unknown disturbances is presented. The residual is generated using full-order state observers （FSO）. Based on an analytical solution to a type of Sylvester matrix equations, the parameterization of the observer gain matrix is given. In terms of the design degrees of freedom provided by the parametric observer design and a group of introduced parameter vectors, a sufficient and necessary condition for fullorder state observer design with disturbance decoupling is then established. By properly constraining the design parameters according to this proposed condition, the effect of the disturbance on the residual signal is also decoupled, and a simple algorithm is developed. The presented approach offers all the degrees of design freedom. Finally, a numerical example illustrates the effect of the proposed approach.

State Feedback Control for a Class of Fractional Order Nonlinear Systems

Using the Lyapunov function method, this paper investigates the design of state feedback stabilization controllers for fractional order nonlinear systems in triangular form, and presents a number of new results. First, some new properties of Caputo fractional derivative are presented, and a sufficient condition of asymptotical stability for fractional order nonlinear systems is obtained based on the new properties. Then, by introducing appropriate transformations of coordinates, the problem of controller design is converted into the problem of finding some parameters, which can be certainly obtained by solving the Lyapunov equation and relevant matrix inequalities. Finally, based on the Lyapunov function method, state feedback stabilization controllers making the closed-loop system asymptotically stable are explicitly constructed. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. © 2014 Chinese Association of Automation.

Low-order harmonic generation of hydrogen molecular ion in laser field studied by the two-state model

The low-order harmonic generation of hydrogen molecular ion interacting with a linearly polarized laser field has been investigated theoretically by using a simple two-state model. The validity of the two-state model is carefully examined by comparing the harmonic spectra of hydrogen molecular ion obtained from this model with those from the three-dimensional time-dependent Schr¨odinger equation. When combined with the Morlet transform of quantum time-frequency spectrum,the two-state model can be used to study the dynamical origin of the low-order harmonic generation of hydrogen molecular ion driven by low-frequency pulses. In addition, some interesting structures of the time profiles for low order harmonics are obtained.

Asymptotical consensus of fractional-order multi-agent systems with current and delay states

In this paper,we study some new fractional-order multi-agent systems with current and delay states (FMASCD).Using the generalized Nyquist's stability criterion and Gerschgorin's circle theorem,we obtain the bounded input-bounded output (BIBO) stability and asymptotical consensus of the FMASCD under mild conditions.Moreover,we give some numerical examples to illustrate our main results.

Influence of the initial electronic state on minima of high-order harmonic spectrum radiated from hydrogen molecular ion

We theoretically investigate the high-order harmonic generation of the one-dimensional hydrogen molecular ion at fixed intermediate internuclear distance, driven by a multicycle laser field. Our results show that the initial electronic state of the hydrogen molecular ion affects the modulation of the high-order harmonic spectrum, especially the positions of the minima. Based on the two-state model, the underlying physical mechanism of the minimum is analyzed and discussed. Further analysis shows that the different positions of the minima in the different initial electronic states can be understood via the different interferences of the two phase-adiabatic states at the ionization times.

Higher-Order Fluctuations and SU(1,1) Higher-Order Squeezing in SU(1,1) Generalized Coherent States

The higher order fluctuations in the SU(1,1) generalized coherent states are discussed. The definition of higher order SU(1,1) squeezing is introduced in terms of higher order uncertainty relation. For two possible bosonic realizations of SU(1,1) Lie algebra, the second , fourth and sixth order SU(1,1) squeezing are examined in detail. It is shown that the SU(1,1) generalized coherent states can be squeezed to not only second order, but also fourth and sixth order. Hence, it follows that the higher order squeezing will occur for the fluctuations of the square of amplitude in squeezed vacuum. SU(1,1) higher order squeezing is a kind of non classical property which is independent of second order squeezing.

面向一统的都城规划——再论隋大兴的空间形制建构及其历史意义

隋大兴是在一统全国过程中规划建设的新都城。其营建不仅在于都城空间本身,也包括以都城为核心面向整个疆域的一系列空间建构。本文分析了中国古代“大一统”思想的发展演变以及隋大兴的建设背景,认为隋初围绕大兴城在疆域范围、近畿区域、都城形态三个层面的一系列空间建构是中国古代“大一统”思想与全国一统进程实际需要相结合的空间政治实践,呼应了当时的军事、政治、经济、文化等需求,丰富和发展了“大一统”理念在都城规划中的表达,提高了都城在国家秩序建构和国家认同形成方面的作用,推动了隋唐“大一统”时代的形成和巩固。

State feedback stabilization for high-order stochastic nonlinear systems with zero dynamics

In this paper, for a class of high-order stochastic nonlinear systems with zero dynamics which are neither necessarily feedback linearizable nor affine in the control input, the problem of state feedback stabilization is investigated for the first time. Under some weaker assumptions, a smooth state feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on [0,∞）, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and all the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.

固体激光器涡旋光束产生实验系统设计与实现

高质量的涡旋光束在量子信息、激光雷达、激光通信等领域有着广泛的应用前景。为了用固体激光器直接产生涡旋光束,该文基于谐振腔模式与激光介质作用的速率方程,阐述了在二极管端面泵浦固体激光器中通过环形光泵浦产生拉盖尔-高斯涡旋光的原理。设计了环形光泵浦固体激光器产生涡旋光的实验方案并搭建了实验系统。实验产生了角向阶次为1阶、2阶的涡旋光束,相位涡旋手性可通过微调谐振腔输出镜调节。该实验能够使学生利用固体激光器直接产生涡旋光束并观察涡旋光束的相位特性,有助于学生加深对激光谐振腔模式理论及涡旋光束相位特性的理解,为相关专业学生的课程教学提供有力支撑。

家国一体:老龄社会治理的中国秩序

老龄社会治理兼具国家力量的制度设计与家庭建设的机制保障,不仅事关家庭的结构变迁或功能弱化的问题,也关乎国家在迈向重度老龄化新国情下的角色定位和职能界定的问题。西方的治理困境及中国的治理实践表明,家国秩序是老龄社会治理的内在逻辑。如果不理解家庭与国家的秩序关系并予以理顺,将无法有效构建老龄社会治理体系。作为一个复杂性议题,中国老龄社会治理的家国秩序不是西方福利国家在“家庭化、去家庭化或再家庭化”的主观意志,而是在“家国同构”的关系共同体下动态的历史演进。以家国一体为典型特征的老龄社会治理的中国秩序,既是尝试对西方福利国家的理论修正,更是面向现代性与人民性的实践表征。