The quantum spectral analysis of the two-dimensional annular billiard system

Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system.

Universality in Statistical Measures of Trajectories in Classical Billiard Systems

For classical billiards, we suggest that a matrix of action or length of trajectories in conjunction with statistical measures, level spacing distribution and spectral rigidity, can be used to distinguish chaotic from integrable systems. As examples of 2D chaotic billiards, we considered the Bunimovich stadium billiard and the Sinai billiard. In the level spacing distribution and spectral rigidity, we found GOE behaviour consistent with predictions from random matrix theory. We studied transport properties and computed a diffusion coefficient. For the Sinai billiard, we found normal diffusion, while the stadium billiard showed anomalous diffusion behaviour. As example of a 2D integrable billiard, we considered the rectangular billiard. We found very rigid behaviour with strongly correlated spectra similar to a Dirac comb. These findings present numerical evidence for universality in level spacing fluctuations to hold in classically integrable systems and in classically fully chaotic systems.

Billiards Optimization Algorithm:A New Game-Based Metaheuristic Approach

Metaheuristic algorithms are one of themost widely used stochastic approaches in solving optimization problems.In this paper,a new metaheuristic algorithm entitled Billiards Optimization Algorithm(BOA)is proposed and designed to be used in optimization applications.The fundamental inspiration in BOA design is the behavior of the players and the rules of the billiards game.Various steps of BOA are described and then its mathematical model is thoroughly explained.The efficiency of BOA in dealing with optimization problems is evaluated through optimizing twenty-three standard benchmark functions of different types including unimodal,high-dimensional multimodal,and fixed-dimensionalmultimodal functions.In order to analyze the quality of the results obtained by BOA,the performance of the proposed approach is compared with ten well-known algorithms.The simulation results show that BOA,with its high exploration and exploitation abilities,achieves an impressive performance in providing solutions to objective functions and is superior and far more competitive compared to the ten competitor algorithms.

具有零曲率边界Billiard系统的混合率(英文)

对具有慢混合率的奇异动力系统的研究方法是近年才发展起来的,但应用到具体模型上还很困难.研究了一类新型的具有0曲率边界的半发散billiards系统,证明了这个系统碰撞映射的相关函数的收敛速率的上界是(lnn)8/3/n5/3,其中n表示离散的时间.

一组Billiard系统的衰减率(英文)

对具有慢混合率的奇异动力系统的研究方法是近几年才发展起来的,但应用到具体模型上还比较困难.研究了一组新型的半发散billiards系统,证明该系统碰撞映射的相关函数的收敛速率的上界为(lnn)3/n2,其中n表示离散时间.

Semiclassical Analysis of Quarter Stadium Billiards

An expansion method for stationary states is applied to obtain the eigenfunctions and the eigenenergies of the quarter stadium billiard, and its nearest energy-level spacing distribution is obtained. The histogram is consistent with the standard Wigner distribution, which indicates that the stadium billiard system is chaotic. Particular attention is paid to pursuing the quantum manifestations of such classical chaos. The correspondences between the Fourier transformation of quantum spectra and classical orbits are investigated by using the closed-orbit theory. The analytical and numerical results are in agreement with the required resolution, which corroborates that the semiclassical method provides a physically meaningful image to understand such chaotic systems.

The quantum spectra analysis of the circular billiards in wells

We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier- transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classlcal method provides a bridge between quantum and classical mechanics.

EQUIDISTRIBUTION OF CLOSED ORBITS OF BILLIARD FLOWS ON THE PLANE

The authors consider the billiard system with finitely many convex scatters with smooth boundary satisfying the visibility assumption on the plane and prove that the closed orbits for the billiard flow is uniformly distributed.

Experimental investigation of the fluctuations in nonchaotic scattering in microwave billiards

We report on the experimental investigation of the properties of the eigenvalues and wavefunctions and the fluctuation properties of the scattering matrix of closed and open billiards, respectively, of which the classical dynamics undergoes a transition from integrable via almost integrable to fully chaotic. To realize such a system, we chose a billiard with a 60° sector shape of which the classical dynamics is integrable, and introduced circular scatterers of varying number, size,and position. The spectral properties of generic quantum systems of which the classical counterpart is either integrable or chaotic are universal and well understood. If, however, the classical dynamics is pseudo-integrable or almost-integrable,they exhibit a non-universal intermediate statistics, for which analytical results are known only in a few cases, e.g., if it corresponds to semi-Poisson statistics. Since the latter is, above all, clearly distinguishable from those of integrable and chaotic systems, our aim was to design a billiard with these features which indeed is achievable by adding just one scatterer of appropriate size and position to the sector billiard. We demonstrated that, while the spectral properties of almostintegrable billiards are sensitive to the classical dynamics, this is not the case for the distribution of the wavefunction components, which was analyzed in terms of the strength distribution, and the fluctuation properties of the scattering matrix which coincide with those of typical, fully chaotic systems.

Level spacing statistics for two-dimensional massless Dirac billiards

Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The search- ing for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation （or Weyl equation） and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.

Semiclassical approximation for transmission through open Sinai billiards

We use a semiclassical approximation to study the transport through the weakly open chaotic Sinai quantum billiards which can be considered as the schematic of a Sinai mesoscopic device,with the diffractive scatterings at the lead openings taken into account.The conductance of the ballistic microstructure which displays universal fluctuations due to quantum interference of electrons can be calculated by Landauer formula as a function of the electron Fermi wave number,and the transmission amplitude can be expressed as the sum over all classical paths connecting the entrance and the exit leads.For the Sinai billiards,the path sum leads to an excellent numerical agreement between the peak positions of power spectrum of the transmission amplitude and the corresponding lengths of the classical trajectories,which demonstrates a good agreement between the quantum theory and the semiclassical theory.

Negative Magneto—Resistance Beyond Weak Localization in Three—Dimensional Billiards：Effect of Arnold Diffusion

We investigate a semiclassical conductance for ballistic open three-dimensional (3-d) billiards. For partially or completely broken-ergodic 3-d billiards such as SO(2) symmetric billiards, the dependence of the conductance on the Fermi wavenumber is dramatically changed by the lead orientation. Application of a symmetry-breaking weak magnetic field brings about mixed phase-space structures of 3-d billiards which ensures a novel Arnold diffusion that cannot be seen in 2-d billiards. In contrast to the 2-d case, the anomalous increment of the conductance should inevitably include a contribution arising from Arnold diffusion as well as a weak localization correction. Discussions are devoted to the physical condition for observing this phenomenon.

Unpredictable Property of a Kicked Billiard Ball

A simultaneous change in the systemic property of a kicked billiard ball is observed from an entirely smooth and conservative state to a piecewise smooth and quasi-dissipative state when a single controlling parameter has been adjusted. The transition induces a sudden change of a typical conservative stochastic web into a transient web. The iterations on the transient web eventually escape to some elliptic islands. In the meantime, a fat fractal forbidden web, which appears also at the threshold, grows up and cuts away increasingly more parts from the original conservative stochastic web. We numerically show that the initial conditions that generated different attractors are mixed in a random manner and the pattern remains unchanged even when smaller and smaller scales are used for examination, indicating a riddle-like basin structure that practically rules out the possibility of predicting the attractors from a given initial condition.

ON UNILATERALLY CONSTRAINED MOTIONS OF RIGID BODIES SYSTEMS

In this paper , the unilaterally constrained motions of a large class of rigid bodiessystems are studied both locally and globally. The main conclusion is that locally,such a system bahaves like a particle in a Riemannian manifold with boundary;globally.under the assumption of energy conservation, the system behaves like a billiards system over a Riemannina manifold with boundary

On Differential Equations of Integrable Billiard Tables

We introduce a method to find differential equations for functions which define tables,such that associated billiard systems admit a local first integral.We illustrate this method in three situations:the case of(locally)integrable wire billiards,for finding surfaces in R^(3)with a first integral of degree one in velocities,and for finding a piece-wise smooth surface in R^(3)homeomorphic to a torus,being a table of a billiard admitting two additional first integrals.

医院不同绩效考核办法的效率分析

简要介绍了几种绩效考核方法,并结合影响考核方法效率的因素,对每种考核方法的实施效率进行了分析。在此基础上提出:医院在设计其考核方法时,应综合考虑各因素对其实施效率的影响,只有根据医院所处的不同发展阶段的特点,选择适合的考核方法,才能达到考核的目的。

3D台球训练考评系统的设计与实现

体育信息化给体育管理和训练带来了很大的帮助。在调研台球训练和考评的实际需要基础上,基于.NET平台和SSH架构,结合Unity3D引擎,设计和实现了一个3D台球训练考评系统。系统可以将台球典型的题目以图形方式保存在计算机中,通过3D界面指导训练者摆球,通过3D动画和视频提示击打要点,通过与鹰眼子系统的通信,对打球者的实际击打过程是否符合要求进行评价。实现训练者反复练习和对训练员以及运动员的标准化实操和理论考试。系统功能全面、界面友好、有很强的实用性。

关于刚体系统的单侧约束运动

本文研究了一大类刚体系统的单侧约束运动的局部和整体性质．主要结论是；局部地，这类系统的运动相当于某带过黎曼流形上的质点的运动；整体地，在能量守恒的假定下．这类系统相当于某带边黎曼流形上的台球系统．

弹球系统的轨迹中点图

建立了弹球系统的轨迹中点图。通过对多种弹球系统模型的分析发现,离散点型的轨迹中点图对应着弹球系统的周期行为,线型的轨迹中点图对应着系统的准周期行为,而由大量弥散点组成的轨迹中点图则对应着系统的混沌行为。研究表明,轨迹中点图能够简便而有效地描述弹球系统的动力学行为。

供电工程 CAD 工作平台的研制

应用ＴＵＲＢＯＣ语言研制了在ＵＣＤＯＳ支持下的供电工程ＣＡＤ软件的主控程序。