From Chaos to Ordering: New Studies in the Shannon Entropy of 2D Patterns

Properties of the Voronoi tessellations arising from random 2D distribution points are reported. We applied an iterative procedure to the Voronoi diagrams generated by a set of points randomly placed on the plane. The procedure implied dividing the edges of Voronoi cells into equal or random parts. The dividing points were then used to construct the following Voronoi diagram. Repeating this procedure led to a surprising effect of the positional ordering of Voronoi cells, reminiscent of the formation of lamellae and spherulites in linear semi-crystalline polymers and metallic glasses. Thus, we can conclude that by applying even a simple set of rules to a random set of seeds, we can introduce order into an initially disordered system. At the same time, the Shannon (Voronoi) entropy showed a tendency to attain values that are typical for completely random patterns; thus, the Shannon (Voronoi) entropy does not distinguish the short-range ordering. The Shannon entropy and the continuous measure of symmetry of the patterns demonstrated the distinct asymptotic behavior, while approaching the close saturation values with the increase in the number of iteration steps. The Shannon entropy grew with the number of iterations, whereas the continuous measure of symmetry of the same patterns demonstrated the opposite asymptotic behavior. The Shannon (Voronoi) entropy is not an unambiguous measure of order in the 2D patterns. The more symmetrical patterns may demonstrate the higher values of the Shannon entropy.     

利用破坏对称性的超导人造原子制备χ型四比特纠缠态

提出了利用在一维传输线共振器中的破坏对称性的超导人造原子来制备χ型四比特纠缠态的方案. 方案中所用到的Δ型三能级人造原子不同于自然的原子, 它可以产生循环跃迁. 经过适当时间的相互作用和简单的操作, 可以得到想要制备的纠缠态. 由于人造原子的激发态和光子态被绝热消除, 所以该方案对于人造原子的自发辐射和传输线共振器的衰减是鲁棒的.     

The effects of cubic potentials on discrete breathers in a mixed Klein－Gordon /Fermi－Pasta－Ulam chain

Nonlinearity has a crucial impact on the symmetry properties of dynamical systems. This paper studies a one-dimensional mixed Klein--Gordon/Fermi--Pasta--Ulam diatomic chain using the expanded rotating plane-wave approximation and numerical calculations to determine the effect of cubic potentials on the symmetry properties of discrete breathers in this system. The results will be very useful to researchers in the field of numerical calculations on discrete breathers.     

An Interacting Gauge Field Theoretic Model for Hodge Theory: Basic Canonical Brackets

We derive the basic canonical brackets amongst the creation and annihilation operators for a two （1 ＋ 1）- dimensional （2D） gauge field theoretic model of an interacting Hodge theory where a U（1） gauge field （Aμ） is coupled with the fermionic Dirac fields （ψ and ψ）. In this derivation, we exploit the spin-statistics theorem, normal ordering and the strength of the underlying six infinitesimal continuous symmetries （and the concept of their generators） that are present in the theory. We do not use the definition of the canonical conjugate momenta （corresponding to the basic fields of the theory） anywhere in our whole discussion. Thus, we conjecture that our present approach provides an alternative to the canonical method of quantization for a class of gauge field theories that are physical examples of Hodge theory where the continuous symmetries （and corresponding generators） provide the physical realizations of the de Rham cohomological operators of differential geometry at the algebraic level.     

Asymmetric nonlinear-mode-conversion in an optical waveguide withPT symmetry

Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics.     

Cl+CHD3(v1=1)的立体化学反应研究 (cited: 2)

最近报道了氯原子从不同方向进攻CHD₃分子的C-H化学键的全方位三维立体化学反应过程,其中通过对偏振相关微分反应截面的测量以及分析,反应物的空间取向对化学反应的影响有了比较清晰的了解．这里,在切片成像满足特定的对称性要求的条件下,通过对两种最常见的反应构型即平行碰撞以及垂直碰撞反应构型的分析,得到三维微分反应截面以及积分反应截面,这两种立体化学反应活性的比较对于理解各向同性的反应物的反应活性有着较大的帮助,也是一般化学家更为感兴趣的课题,从而可以加深关于化学反应过程的直观认识以及探讨     

The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

Quasi-normal modes of extremal black holes from hidden conformal symmetry

In this Letter, we construct the quasi-normal modes of three-dimensional extremal black holes in an algebraic way. We show that the infinite towers of the quasi-normal modes of scalar, vector and tensor could be constructed as the descendents of the highest weight modes. Our investigation shows that the hidden conformal symmetry suggested in Chen et al. (2010) [5] is an intrinsic property of the extremal black hole. Moreover, we notice that we need to fix the freedom in defining the local vector fields and find the right hidden conformal symmetry to obtain the physical quasi-normal modes.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.