Topology and geometry of nematic braids

Topological analysis of disclinations in nematic liquid crystals is an interesting and diverse topic that goes from strict mathematical theorems to applications in elaborate systems found in experiments and numerical simulations. The theory of nematic disclinations is shown from both the geometric and topological perspectives. Entangled disclination line networks are analyzed based on their shape and the behavior of their cross section. Methods of differential geometry are applied to derive topological results from reduced geometric information. For nematic braids, systems of −1/2 disclination loops, created by inclusion of homeotropic colloidal particles, a formalism of rewiring is constructed, allowing comparison and construction of an entire set of different conformations. The disclination lines are described as ribbons and a new topological invariant, the self-linking number, is introduced. The analysis is generalized from a constant −1/2 profile to general profile variations, while retaining the geometric treatment. The workings of presented topological statements are demonstrated on simple models of entangled nematic colloids, estimating the margins of theoretical assumptions made in the formal derivations, and reviewing the behavior of the disclinations not only under topological, but also under free-energy driven constraints.     

A geometric Birkhoffian formalism for nonlinear RLC networks

The aim of this paper is to give a formulation of the dynamics of nonlinear RLC circuits as a geometric Birkhoffian system and to discuss in this context the concepts of regularity, conservativeness, dissipativeness. An RLC circuit, with no assumptions placed on its topology, will be described by a family of Birkhoffian systems, parameterized by a finite number of real constants which correspond to initial values of certain state variables of the circuit. The configuration space and a special Pfaffian form, called the Birkhoffian, are obtained from the constitutive relations of the resistors, inductors and capacitors involved and from Kirchhoff’s laws. Under certain assumptions on the voltage–current characteristic for resistors, it is shown that a Birkhoffian system associated with an RLC circuit is dissipative. For RLC networks which contain a number of pure capacitor loops or pure resistor loops the Birkhoffian associated is never regular. A procedure for reducing the original configuration space to a lower dimensional one, thereby regularizing the Birkhoffian, it is also presented. In order to illustrate the results, specific examples are discussed in detail.     

Configurational statistics of densely and fully packed loops in the negative-weight percolation model

By means of numerical simulations we investigate the configurational properties of densely and fully packed configurations of loops in the negative-weight percolation (NWP) model. In the presented study we consider 2d square, 2d honeycomb, 3d simple cubic and 4d hypercubic lattice graphs, where edge weights are drawn from a Gaussian distribution. For a given realization of the disorder we then compute a configuration of loops, such that the configurational energy, given by the sum of all individual loop weights, is minimized. For this purpose, we employ a mapping of the NWP model to the “minimum-weight perfect matching problem” that can be solved exactly by using sophisticated polynomial-time matching algorithms. We characterize the loops via observables similar to those used in percolation studies and perform finite-size scaling analyses, up to side length L = 256 in 2d, L = 48 in 3d and L = 20 in 4d (for which we study only some observables), in order to estimate geometric exponents that characterize the configurations of densely and fully packed loops. One major result is that the loops behave like uncorrelated random walks from dimension d = 3 on, in contrast to the previously studied behavior at the percolation threshold, where random-walk behavior is obtained for d ≥ 6.     

Exceptional points in multichannel resonance quantization

We derive from the quantization condition of a multichannel resonance problem the behaviour of resonance energies close to an exceptional point (EP) where two resonance energies coalesce. The formalism is applied to a one-dimensional model of the molecular ion H₂ ⁺. Although the approach does not use a matrix diagonalization procedure, all known results about exceptional points are present, including the transfer from one resonance to another when following a loop encircling the EP. We study how the resonance wave functions behave along loops around the EP, as well as the associated geometric phases.     

Fundamentals in generalized elasticity and dislocation theory of quasicrystals: Green tensor,dislocation key-formulas and dislocation loops

The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura–Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach–Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach–Koehler stress formula, Mura–Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals.     

小尺寸正方形铁磁薄膜边界效应对磁化翻转过程的影响

用自旋动力学方法系统地研究磁偶极相互作用表现的边界效应对小尺寸正方形铁磁薄膜的磁化翻转过程的影响.在确定的磁偶极相互作用强度下,针对不同的单轴各向异性强度和不同的磁化角(外磁场与易轴间的夹角),具体给出矫顽场与磁化角及单轴各向异性强度之间的依赖关系和-些有代表性的磁滞回线,并给出磁化翻转过程中-些有代表性的微观磁结构.模拟结果表明:磁偶极相互作用表现的边界钉扎作用与单轴各向异性场之间的竞争决定磁滞回线的形状和矫顽场的大小,从而在不同磁化角情况下会导致不同的矫顽场机理.本文提出可有效地描述正方形铁磁性薄膜复杂微观磁畴结构的形成与演变的五磁畴模型.这种五磁畴模型既能直接揭示单轴各向异性正方形铁磁薄膜的几何特性和物理特性,也方便于磁化翻转过程的分析.     

Entanglement entropy in Abelian gauge theories

The definition of geometric entanglement entropy associated with some region in space is discussed for the case of gauge theories. It is argued that since in gauge theories elementary excitations look like loops (closed electric strings) rather than points (particles), the boundaries of the regions should also carry some nonzero entropy. This entropy counts the number of strings which cross these boundaries. Explicit calculations of such entropy are carried out in the limits of infinitely strong and weak couplings of three- and four-dimensional Z _N gauge theories. In three dimensions we find that the entropy is a constant which does not depend on the region, while in four dimensions the familiar area law for the entropy is recovered.     

Geometric phases and Mielnik's evolution loops

The cyclic evolutions and associated geometric phases induced by time-independent Hamiltonians are studied for the case when the evolution operator becomes the identity (those processes are called evolution loops). We make a detailed treatment of systems having equally-spaced energy levels. Special emphasis is made on the potentials which have the same spectrum as the harmonic oscillator potential (the generalized oscillator potentials) and on their recently found coherent states.     

光纤Sagnac干涉仪中单光子干涉及路由控制

介绍一种光纤中稳定的单光子干涉以及单光子路由控制方式. 使用Sagnac单光子环形干涉仪，通过分时相位调制，改变其顺时针和逆时针两路光子间的相位差. 在Sagnac单光子环形干涉仪中，顺时针和逆时针两路光子走过的是同一段光纤，简便有效地补偿了光纤长度随时间缓变带来的相位涨落，而且两路光子经历了相同的偏振模色散，较好地抑制了偏振态波动对单光子干涉的影响. 在长达5km的1550nm单模光纤中，获得大于98%的单光子干涉和大于90%单光子路由控制；在长度为27和50km光纤环路中，分别获得大于94%和84%单 关键词： 单光子路由 单光子干涉 Sagnac单光子环形干涉仪 量子保密通信     

Instability of interstitial dislocation loops in electron-irradiated dielectrics

The experiments on electron irradiation of yttrium-stabilized zirconium oxide samples show the formation of strong elastic fields near interstitial dislocation loops. The fields increase with an increase in the loop radius and, when the loop radius reaches a certain critical value, the loops became unstable due to the beginning of plastic deformation and the formation of a dislocation network. The mechanism of the occurrence of this instability is suggested. It is based on the accumulation of charges at dislocation loops due to ionization processes in an electron-irradiated dielectric. It is shown that the accumulation of the electric charge at growing dislocation loops in dielectrics may be responsible for an increase in elastic stresses near dislocation loops and for their instability because of the beginning of plastic deformation near the loops when stresses at growing loops become close to the theoretical yield stress of the material.     

Cooperative nucleation of shear dislocation loops

The mean elastic interaction between randomly distributed transient subcritical shear loops of the same sign, formed in the presence of an applied shear stress, is the "image stress." This stress is proportional to the volume density of loops and has the same sign as the applied stress. The image stress promotes the cooperative nucleation of shear loops, and leads to an instability in which the number of loops and the image stress increase rapidly, leading to the generation of stable expanding loops. The critical stress at which the instability is predicted is relatively high.     

Detecting non-Abelian geometric phases with superconducting nanocircuits

We propose a feasible scheme to detect the noncommutative feature of non-Abelian geometric phases (NAGP) with superconducting nanocircuits. The induced NAGP associated with two-fold degenerate states naturally arises in the chosen four-level subsystem interacting with the microwave pulses. We explicitly show the noncommutative effect of the NAGP by considering the difference between the level populations at the end of the composed evolution loops l₂l₁ and the counter-ordered one l₁l₂. The scheme opens the new possibility for detecting the fundamental characteristics of the NAGP with superconducting circuit devices.     

氢离子辐照纯钒中形成的位错环

钒合金作为聚变堆候选材料, 其辐照损伤行为一直是关注的重点. 研究辐照时形成的位错环的性质, 其意义在于揭示纯钒中辐照空洞的长大机理. 这种机理表现为不同类型位错环对点缺陷吸收的偏压不同, 从而影响金属的辐照肿胀. 本文利用加速器对纯钒薄膜样品进行氢离子辐照, 然后, 利用透射电镜的inside-outside方法分析氢离子辐照所形成的位错环的类型. 结果表明, 在氢离子辐照纯钒中没有发现柏氏矢量b=<110>的位错环, 只有柏氏矢量b=1/2<111>和b=<110>的位错环, 这两种位错环的惯性面处于{110}-{112}之间. 能确定性质的位错环全部为间隙型位错环, 未发现空位型位错环.     

Elastic-energy relaxation in heterostructures with strained nanoinclusions

Elastic-energy relaxation in systems with nanoinclusions is considered. The relaxation is related to the formation of the following dislocation loops: a single misfit dislocation loop or a group of such loops on the matrix-nanoinclusion interface and/or a satellite dislocation loop near the inclusion. The critical inclusion sizes beginning from which misfit dislocation loops and satellite dislocation loops can nucleate are determined for various models of relaxation processes. The dependences of the satellite-dislocation-loop diameter on the inclusion size are calculated and compared with experimental data.     

The remagnetization process in spin-valve structures

The process of magnetization reversal in ultrathin magnetic trilayer is analyzed. It is shown that the shape of magnetization hysteresis loops and the giant magnetoresistance essentially depend on the relative magnitudes of magnetic parameters of the top and the bottom layers. New types of hysteresis loops are found for characteristic relative magnitudes of the parameters. Analysis of the dependence of the shape of hysteresis loops on the magnitude of interlayer exchange is performed. The phase diagram which determines the regions of existence of characteristic hysteresis loops for different relative magnitudes of the uniaxial anisotropy constant and exchange constant J₁ is constructed.     

On a sharp transition from area law to perimeter law in a system of random surfaces

We introduce and study a phase transition which is associated with the spontaneous formation of infinite surface sheets in a Bernoulli system of random plaquettes. The transition is manifested by a change in the asymptotic behavior of the probability of the formation of a surface, spanning a prescribed loop. As such, this transition offers a generalization of the bond percolation phenomenon. At low plaquette densities, the probability for large loops is shown to decay exponentially with the loops' area, whereas for high densities the decay is by a perimeter law. Furthermore, we show that the two phases of the three dimensional plaquette system are in a precise correspondence with the two phases of the dual system of random bonds. Thus, if a natural conjecture about the phase structure of the bond percolation model is true, then there is a sharp transition in the asymptotic behavior of the surface events. Our analysis incorporates block variables, in terms of which a non-critical system is transformed into one which is close to a trivial, high or low density, fixed point. Stochastic geometric effects like those discussed here play an important role in lattice gauge theories.     

“Loop the loop”

The applicability of the collective coordinate method (saddle-point approximation) for large-N planar models is discussed. Some unstated assumptions are clarified. Statements that Wilson loops form a complete set of gauge invariant operators are also examined and a set of generalized algebraic Mandelstam relations among Wilson loops is presented. The inclusion of loops that wind around themselves and cross many times, as independent variables, is stressed.     

空位位错环的形成

本文研究了淬火面心立方金属内位错环和空洞的形核和长大问题。两种核都能形成,但是位错环的长大速度比空洞的长大速度大很多倍,故电子显微镜能看清的大缺陷都是位错环,而不是空洞。