Tri-polarized MIMO systems in real-world channels: Channel investigation and performance analysis

Polarized multi-antenna systems are an effective solution for reducing inter-antenna spacing while still maintaining low inter-antenna correlation. Traditionally, only dual-polarized antenna systems are used for polarized transceivers. In this paper, tri-polarized antenna systems are investigated. Starting from the polarization mechanisms in the wireless propagation channel, it is shown that dual-polarized MIMO systems show high sensitivity to the transmitter and receiver orientation, which may be very critical in practical applications. Tri-polarized MIMO systems are introduced as a solution to obtain a robust MIMO performances, which are independent of the transmitter and receiver orientation. The performances of dual- and tri-polarized MIMO systems are evaluated on real-world measured channels, and the limits of each of these systems is highlighted.     

单面完整约束系统的速度依赖对称性与Lutzky守恒量

研究单面完整约束系统的对称性与守恒量.给出单面完整约束系统Lie对称性的定义，得到了由依赖于速度的一般Lie对称性直接导致的Lutzky守恒量，并给出了它的若干特例：有多余坐标的完整约束系统、非保守力学系统、Lagrange系统的Lutzky守恒量.并举例说明结果的应用. 关键词： 分析力学 单面约束 Lie对称性 Lutzky守恒量     

Stationary solutions of Liouville equations for non-Hamiltonian systems

We consider the class of non-Hamiltonian and dissipative statistical systems with distributions that are determined by the Hamiltonian. The distributions are derived analytically as stationary solutions of the Liouville equation for non-Hamiltonian systems. The class of non-Hamiltonian systems can be described by a non-holonomic (non-integrable) constraint: the velocity of the elementary phase volume change is directly proportional to the power of non-potential forces. The coefficient of this proportionality is determined by Hamiltonian. The constant temperature systems, canonical-dissipative systems, and Fermi-Bose classical systems are the special cases of this class of non-Hamiltonian systems.     

相对论Birkhoff系统的平衡稳定性

研究相对论Birkhoff系统的平衡稳定性.给出相对论Birkhoff自治系统、半自治系统和非自治系统的平衡方程、受扰运动方程和一次近似方程;给出判定平衡稳定性的一次近似方法及其判据;讨论相对论Birkhoff系统平衡稳定性和经典Birkhoff系统平衡稳定性的关系.给出实例以说明方法的应用 关键词： 相对论 Birkhoff系统 平衡稳定性 一次近似方法     

Type II quantum chaos

A classification of quantum systems into three categories, type I, II and III, is proposed. The classification is based on the degree of sensitivity upon initial conditions, and the appearance of chaos. The quantum dynamics of type I systems is quasi periodic displaying no exponential sensitivity. They arise, e.g., as the quantized versions of classical chaotic systems. Type II systems are obtained when classical and quantum degrees of freedom are coupled. Such systems arise naturally in a dynamic extension of the first step of the Born-Oppenheimer approximation, and are of particular importance to molecular and solid state physics. Type II systems can show exponential sensitivity in the quantum subsystem. Type III systems are fully quantized systems which show exponential sensitivity in the quantum dynamics. No example of a type III system is currently established. This paper presents a detailed discussion of a type II quantum chaotic system which models a coupled electronic-vibronic system. It is argued that type II systems are of importance for any field systems (not necessarily quantum) that couple to classical degrees of freedom.     

Differential System＇s Nonlinear Behaviour of Real Nonlinear Dynamical Systems

Chaos attractor behaviour is usually preserved if the four basic arithmetic operations, i.e. addition, subtraction, multiplication, division, or their compound, are applied. First-order differential systems of one-dimensional real discrete dynamical systems and nonautonomous real continuous-time dynamical systems are also dynamical systems and their Lyapunov exponents are kept, if they are twice differentiable. These two conclusions are shown here by the definitions of dynamical system and Lyapunov exponent. Numerical simulations support our analytical results. The conclusions can apply to higher order differential systems if their corresponding order differentials exist.     

Dynamics of Hamiltonian systems under piecewise linear forcing

A two-parameter family of smooth Hamiltonian systems perturbed by a piecewise linear force is analyzed. The systems are represented both as maps and as dynamical systems. Currently available analytical and numerical results concerning the onset of chaos and global diffusion in such systems are reviewed. Dynamical behavior that has no analogs in the class of systems with analytic Hamiltonians is described. A comparison with the well-studied dynamics of a driven pendulum is presented, and essential differences in dynamics between smooth and analytic systems are highlighted.     

Hyperchromats with linear dependence of longitudinal chromatic aberration on wavelength

Optical lens systems that are characterized by a chromatic aberration of a predefined form are called hyperchromats. Our work describes a theory of hyperchromats with a linear dependence of longitudinal chromatic aberration on wavelength. The equations are derived for calculation of basic design parameters of these optical systems and some examples of hyperchromatic optical systems are shown. Mentioned optical systems can be used especially in 3D imaging systems and confocal microscopy.     

Integrating Factors and Conservation Laws for Relativistic Mechanical System

In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativisticmechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generaized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.     

On Chaotification of Discrete Lagrange Systems

This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions.     

Integrating Factors and Conservation Laws for Relativistic Mechanical System

In this paper, we present a new method to construct the conservation laws for relativistic mechanical systems by finding corresponding integrating factors. First, the Lagrange equations of relativistic mechanical systems are established, and the definition of integrating factors of the systems is given; second, the necessary conditions for the existence of conserved quantities of the relativistic mechanical systems are studied in detail, and the relation between the conservation laws and the integrating factors of the systems is obtained and the generalized Killing equations for the determination of the integrating factors are given; finally, the conservation theorem and its inverse for the systems are established, and an example is given to illustrate the application of the results.     

Symplectic-energy-first integrators of discrete mechanico-electrical dynamical systems

A discrete total variation calculus with variable time steps is presented for mechanico-electrical systems where there exist non-potential and dissipative forces. By using this discrete variation calculus, the symplectic-energy-first integrators for mechanico-electrical systems are derived. To do this, the time step adaptation is employed. The discrete variational principle and the Euler--Lagrange equation are derived for the systems. By using this discrete algorithm it is shown that mechanico-electrical systems are not symplectic and their energies are not conserved unless they are Lagrange mechanico-electrical systems. A practical example is presented to illustrate these results.     

统计物理和复杂系统专题编者按

从20世纪中叶至今,复杂系统研究迅速发展,成为了引人注目并具有广泛应用的新领域.复杂系统要么具有结构的复杂性,要么具有演化的复杂性,在多数情况下二者兼具.不同于传统物理学通常处理的规则介质,许多复杂系统具有复杂结构,近年来受到极大关注的复杂网络结构就是其中最典型的代表.同时复杂系统也可表现为演化行为的多样性和复杂性.即便系统结构并不复杂,系统中的非线性相互作用可能产生复杂的演化行为,包括:形形色色的不稳定性;丰富的斑图动力学;各种各样的自组织、涌现及进化行为等等.物理学从一开始就深深进入了复杂系统研究领域,其中统计物理无疑是研究和理解复杂系统最主要的工具.     

光学系统的偏振像差分析

偏振像差是影响光学系统性能的重要因素之一,尤其对偏振有严格要求的光学系统来说更是如此。论述了偏振像差的理论和偏振光线追迹的方法,并对旋转对称光学系统、倾斜偏轴光学系统的偏振像差进行了分析,指出了薄膜设计对偏振像差所产生的重要影响。介绍了提高光学系统偏振精度的几个方法,包括尽可能的减小入射角、薄膜设计的优化和像差之间的相互平衡。     

Diffusion Monte Carlo calculations ofthree-body systems

The application of the diffusion Monte Carlo algorithm in three-body systems is studied. We develop a program and use it to calculate the property of various three-body systems. Regular Coulomb systems such as atoms, molecules, and ions are investigated. The calculation is then extended to exotic systems where electrons are replaced by muons. Some nuclei with neutron halos are also calculated as three-body systems consisting of a core and two external nucleons. Our results agree well with experiments and others' work.     

Nontraditional ordered structures in condensed-matter physics

The so-called nontraditional ordered crystal systems are of particular interest between other ordered systems. With respect to their structure and properties, they are connecting links between the three main groups of condensed matter: periodic systems, aperiodic systems (partially or completely disordered), and biopolymers and living matter.     

动力学系统Noether对称性的几何表示

利用现代微分几何方法研究了Lagrange系统、Hamilton系统和Birkhoff系统的Noether对称性,并导出系统相应的Noether守恒量,最后给出了应用算例.     

Birkhoff系统约化的Routh方法

研究Birkhoff系统的约化.首先,列出系统的运动微分方程及其循环积分;其次,构造Birkhoff系统的Routh函数组,利用循环积分约化Birkhoff系统的运动微分方程,并使约化后的动力学方程仍保持Birkhoff方程的形式;最后,举例说明结果的应用. 关键词： Birkhoff系统 约化 循环积分     

Universal features of hydrodynamic Lyapunov modes in extended systems with continuous symmetries

Numerical and analytical evidence is presented to show that hydrodynamic Lyapunov modes (HLMs) do exist in lattices of coupled Hamiltonian and dissipative maps. More importantly, we find that HLMs in these two classes of systems are different with respect to their spatial structure and their dynamical behavior. To be concrete, the corresponding dispersion relations of Lyapunov exponent versus wave number are characterized by lambda approximately k and lambda approximately k2, respectively. The HLMs in Hamiltonian systems are propagating, whereas those of dissipative systems show only diffusive motion. Extensive numerical simulations of various systems confirm that the existence of HLMs is a very general feature of extended dynamical systems with continuous symmetries and that the above-mentioned differences between the two classes of systems are universal in large extent.     

Group structure analysis for classical lattice systems with constraints: I. General properties

The group structure associated with lattice systems without constraints is extended to systems with constraints and some of its physical consequences are investigated. In particular low- and high-temperature expansions, equilibrium equations and duality transformations are analyzed within this framework. It is shown that a large class of systems with constraints whose configuration space has a group structure are “equivalent” to systems without constraints. These structures are illustrated with several examples.