准晶结构的激光全息人工制作

报道了用激光全息刻写技术结合感光聚合材料体系制作介观尺度二维准周期结构(准晶). 并在前期工作的基础上，研究了不同曝光量对二维空气柱孔径的影响，不同偏振对准晶结构花样的影响. 实验结果显示，可以制作的二维准晶的空气柱孔径可达100nm，而且结构均匀，无缺陷面积大. 用此实验系统可以制作多种花样二维甚至是三维准晶结构. 目前，除激光全息刻写技术外，用其他传统精密机械加工技术来人工制作介观准晶体尚存在很大挑战性. 关键词： 准晶结构 光子晶体 激光全息技术     

Differential Equations Invariant Under Conditional Symmetries

Nonlinear PDE’s having given conditional symmetries are constructed. They are obtained starting from the invariants of the conditional symmetry generator and imposing the extra condition given by the characteristic of the symmetry. Series of examples starting from the Boussinesq and including non-autonomous Korteweg–de Vries like equations are given to show and clarify the methodology introduced.     

Quasicrystals: A Matter of Definition

It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.     

Asymptotic Symmetries in Cosmological Models

In the present article we study asymptotic isometries and asymptotic conformal Killing motions of some anisotropic Bianchi cosmological models. We show that asymptotically isotropic homogeneous cosmological spaces can be covariantly studied and characterized using scalars constructed with the help the Killing equations. We exhibit some illustrative examples of space-times possessing asymptotic Killing collineations. We apply our results in order to discuss asymptotic symmetries associated with scalar cosmological perturbations.     

Symmetries and motions in manifolds

In these lectures the relations between symmetries, Lie algebras, Killing vectors and Noether's theorem are reviewed. A generalisation of the basic ideas to include velocity-dependent co-ordinate transformations naturally leads to the concept of Killing tensors. Via their Poisson brackets these tensors generate an a priori infinite-dimensional Lie algebra. The nature of such infinite algebras is clarified using the example of flat space-time. Next the formalism is extended to spinning space, which in addition to the standard real co-ordinates is parametrised also by Grassmann-valued vector variables. The equations for extremal trajectories (“geodesics”) of these spaces describe the pseudo-classical mechanics of a Dirac fermion. We apply the formalism to solve for the motion of a pseudo-classical electron in Schwarzschild space-time.     

Laws, Symmetries, and Reality

It is argued that quantum mechanics follows naturally from the assumptions that there are no fundamental causal laws but only probabilities for physical processes that are constrained by symmetries, and reality is relational in the sense that an object is real only in relation to another object that it is interacting with. The first assumption makes it natural to include in the action for a gauge theory all terms that are allowed by the symmetries, enabling cancellation of infinities, with only the terms in the standard model observable at the energies at which we presently do our experiments. In this approach, it is also natural to have an infinite number of fundamental interactions.     

Symmetries of Energy-Momentum Tensor： Some Basic Facts

It has been pointed out by Hall et al. [Gen. Rel. Gray. 28 （1996） 299.] that matter collineations can be defined by using three different methods. But there arises the question whether one studies matter collineations by using LεTab=0, or LεT^ab = 0 or LεT^b a=0. These alternative conditions are, of. course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.     

Lie Symmetries of Ishimori Equation

The Ishimori equation is one of the most important(2+1)-dimensional integrable models,which is an integrable generalization of(1+1)-dimensional classical continuous Heisenberg ferromagnetic spin equations.Based on importance of Lie symmetries in analysis of differential equations,in this paper,we derive Lie symmetries for the Ishimori equation by Hirota's direct method.     

Classical Lattice-Gas Models of Quasicrystals

One of the fundamental problems of quasicrystals is to understand their occurrence in microscopic models of interacting particles. We review here recent attempts to construct stable quasicrystalline phases. In particular, we compare two recently constructed classical lattice-gas models with translation-invariant interactions and without periodic ground-state configurations. The models are based on nonperiodic tilings of the plane by square-like tiles. In the first model, all interactions can be minimized simultaneously. The second model is frustrated; its nonperiodic ground state can arise only by the minimization of the energy of competing interactions. We put forward some hypotheses concerning stabilities of nonperiodic ground states. In particular, we introduce two criteria, the so-called strict boundary conditions, and prove their equivalence to the zero-temperature stability of ground states against small perturbations of potentials of interacting particles. We discuss the relevance of these conditions for the low-temperature stability, i.e., for the existence of thermodynamically stable nonperiodic equilibrium states.     

Hybrid Quasicrystals,Transport and Localization in Products of Minimal Sets

We consider convex combinations of finite-valued almost periodic sequences (mainly substitution sequences) and put them as potentials of one-dimensional tight-binding models. We prove that these sequences are almost periodic. We call such combinations hybrid quasicrystals and these studies are related to the minimality, under the shift on both coordinates, of the product space of the respective (minimal) hulls. We observe a rich variety of behaviors on the quantum dynamical transport ranging from localization to transport. CRdO thanks the partial support by CNPq     

十二次对称准周期结构的自相似变换及准晶胞构造

研究十二次对称准晶体模型的几何结构性质.修正了Socolar在正方形-菱形-六边形拼图模型中自相似变换的错误.在Stampfli-Ghler正方形-菱形-三角形拼图模型的基础上,成功地构造出了准晶胞,使得十二次对称准周期结构可以用覆盖理论描述. 关键词： 准晶体 拼图模型 自相似变换 覆盖理论     

Pseudo-Hermitian Hamiltonians and Generalized Involutory Symmetries

We propose definitions of generalized parity (P), time-reversal (T) and charge-conjugation (C) operators such, that any diagonalizable pseudo-Hermitian Hamiltonian is invariant under the involutory symmetries C, TP, and CPT. We inquire about the peculiarities of such symmetries showing that these constitute the P-unitary and P-antiunitary symmetry generators. Moreover, we give a necessary and sufficient condition for diagonalizable pseudo-Hermitian Hamiltonians to admit P-pseudounitary and P-pseudoantiunitary symmetries.     

Lie Symmetries for Hamiltonian Systems Methodological Approach

This paper proposes an algorithm for the Lie symmetries investigation in the case of a 2D Hamiltonian system. General Lie operators are deduced firstly and, in the the next step, the associated Lie invariants are derived. The 2D Yang-Mills mechanical model is chosen as a test model for this method. PACS: 05.45.-a; 02.30.Ik     

Substitutions of vertex configuration of Ammann-Beenker tiling in framework of Ammann lines

The Ammann-Beenker tiling is a typical model for two-dimensional octagonal quasicrystals. The geometric properties of local configurations are the key to understanding its formation mechanism. We study the configuration correlations in the framework of Ammann lines, giving an in-depth inspection of this eightfold symmetric structure. When both the vertex type and the orientation are taken into account, strict confinements of neighboring vertices are found. These correlations reveal the structural properties of the quasilattice and also provide substitution rules of vertex along an Ammann line.     

Permutation Representations Defined by G-Clusters with Application to Quasicrystals

Starting from each finite union of orbits (called G- cluster) of an R-irreducible orthogonal representation of a finite group G, we define a representation of G in a higher-dimensional space (called permutation representation), and we prove that it can be decomposed into an orthogonal sum of two representations such that one of them is equivalent to the initial representation. This decomposition allows us to use the strip projection method and to obtain some patterns useful in quasicrystal physics. We show that certain self-similarities of such a pattern can be obtained by using the decomposition into R-irreducible components of the corresponding permutation representation, and we present two examples.     

Rosenberg问题的对称性与守恒量

Rosenberg问题是一个典型而不太复杂的非完整系统问题.本文利用非完整系统的Noether对称性理论来求这个非完整力学问题的守恒量,进而得到问题的最终解.     

Exotic Hadrons and Underlying Z2,3 Symmetries

The recent observation of higher quark combinations, tetraquarks and pentaquarks, is a strong indication of more exotic hadrons. Using Z₂ and Z₃ symmetries and standard model data, a general quark combination producing new hadronic states is proposed in terms of polygon geometries according to the Dynkin diagrams of  _n affine Lie algebras. It has been shown that Z_2,3 invariance is crucial in the determination of the mesonic or the baryonic nature of these states. The hexagonal geometry is considered in some details producing both mesonic and baryonic states. A general class of this family is also presented.     

D相准晶显示强烈的各向异性电—声子质量增强效应

对ＡｌＮｉＣｏＤ相准晶和热电势测量表明，沿准晶面的电－声子质量增强效应比沿周期方向要大一个数量级以上。     

Algebras of Random Operators Associated to Delone Dynamical Systems

We carry out a careful study of operator algebras associated with Delone dynamical systems. A von Neumann algebra is defined using noncommutative integration theory. Features of these algebras and the operators they contain are discussed. We restrict our attention to a certain C ^*-subalgebra to discuss a Shubin trace formula.     

Noether Symmetries Versus Killing Vectors and Isometries of Spacetimes

Symmetries of spacetime manifolds which are given by Killing vectors are compared with the symmetries of the Lagrangians of the respective spacetimes. We find the point generators of the one parameter Lie groups of transformations that leave invariant the action integral corresponding to the Lagrangian (Noether symmetries). In the examples considered, it is shown that the Noether symmetries obtained by considering the Larangians provide additional symmetries which are not provided by the Killing vectors. It is conjectured that these symmetries would always provide a larger Lie algebra of which the KV symmetres will form a subalgebra. PACS: 04.25.-g, 02.20.Sv, 11.30.-j