Variable Separation and Exact Separable Solutions for Equations of Type uxt=A(u,ux)uxx+B(u,ux)

The generalized conditional symmetry is developed to study the variable separation for equations of type u_xt=A(u,u_x)u_xx+B(u,u_x). Complete classification of those equations which admit derivative-dependent functional separable solutions is obtained and some of their exact separable solutions are constructed.     

Non-Noether Conserved Quantity of Poincaré-Chetaev Equations of a Generalized Classical Mechanics

In the present paper the Lie symmetrical non-Noether conserved quantity of the Poincaré-Chetaev equations of a generalized classical mechanics under the general infinitesimal transformations of Lie groups is discussed. First, we establish the determining equations of Lie symmetry of the equations. Second, the Lie symmetrical non-Noether conserved quantity of the equations is deduced. Finally, an example is given to illustrate the application of the results.     

A Testable Theory for the Emergence of the Classical World

The transition from the quantum to the classical world is not yet understood. Here, we take a new approach. Central to this is the understanding that measurement and actualization cannot occur except on some specific basis. However, we have no established theory for the emergence of a specific basis. Our framework entails the following: (i) Sets of N entangled quantum variables can mutually actualize one another. (ii) Such actualization must occur in only one of the 2^N possible bases. (iii) Mutual actualization progressively breaks symmetry among the 2^N bases. (iv) An emerging “amplitude” for any basis can be amplified by further measurements in that basis, and it can decay between measurements. (v) The emergence of any basis is driven by mutual measurements among the N variables and decoherence with the environment. Quantum Zeno interactions among the N variables mediates the mutual measurements. (vi) As the number of variables, N, increases, the number of Quantum Zeno mediated measurements among the N variables increases. We note that decoherence alone does not yield a specific basis. (vii) Quantum ordered, quantum critical, and quantum chaotic peptides that decohere at nanosecond versus femtosecond time scales can be used as test objects. (viii) By varying the number of amino acids, N, and the use of quantum ordered, critical, or chaotic peptides, the ratio of decoherence to Quantum Zeno effects can be tuned. This enables new means to probe the emergence of one among a set of initially entangled bases via weak measurements after preparing the system in a mixed basis condition. (ix) Use of the three stable isotopes of carbon, oxygen, and nitrogen and the five stable isotopes of sulfur allows any ten atoms in the test protein to be discriminably labeled and the basis of emergence for those labeled atoms can be detected by weak measurements. We present an initial mathematical framework for this theory, and we propose experiments.     

香花石形态所反映的一种可能的孪晶结构

香花石是我国发现的第一个新矿物,它的形态非常复杂.本文基于香花石形态上出现了左形与右形相聚的现象,对香花石形态进行了重新思考,认为同一单形的左形与右形不能相聚形成单晶体,只能形成孪晶,因此,对原香花石晶体图进行了一些修正,认为原香花石晶体图可能是一个孪晶图.这对深入认识晶体形态及晶体对称理论、澄清长期以来人们并没有足够重视的一些基本概念有重要意义.     

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