广义Fibonacci准周期链能谱性质

本文研究一种广义Fibonacci准周期链(孪生子模型)的电子及声子谱。重整化群分析表明,电子能谱具有3分支的自相似结构,但每一层中的中间子带又类似于周期系统。数值计算结果证明这种分析的正确性。对于声子谱,则显示出与Fibonacci链相同的性质。 关键词：     

广义Fibonacci准周期结构声子晶体透射性质的研究

提出了一维广义Fibonacci准周期结构的声子晶体模型. 对弹性波通过该一维准周期结构声子晶体的透射系数进行数值计算,并与周期结构和标准Fibonacci准周期结构声子晶体的透射系数进行比较. 结果表明,利用一维广义Fibonacci准周期结构的声子晶体可获得比周期结构和标准Fibonacci准周期结构声子晶体更大的带隙范围,同时在带隙内有更丰富的局域模式存在. 对局域模性质的研究有助于声波或弹性波滤波器的制作. 关键词： 广义Fibonacci准周期结构 声子晶体 局域化     

斐波那契序列与准晶态

本文从兔子繁殖的数学问题谈起,引入Fibonacci数列.研究了晶体的准周期结构,表明它与Fibonacci数列有密切的关系.     

一维压电Fibonacci类准周期声子晶体传输特性

基于传输矩阵法研究了一维压电Fibonacci类准周期声子晶体的传输特性, 比较了一维Fibonacci序列压电准周期声子晶体与非压电准周期声子晶体以及压电周期性声子晶体的透射性. 计算结果表明:弹性波通过一维准周期结构压电声子晶体时与周期性声子晶体一样会有带隙的出现, 且发现具有压电性的Fibonacci序列准周期声子晶体禁带宽度发生了展宽. 进一步讨论了入射角度对固定频率下声子透射系数的影响,结果表明一维压电Fibonacci序列准周期结构声子透射性依赖于入射角度的选取.     

缺陷对准周期磁超晶格输运性质的影响

研究了缺陷结构的Fibonacci磁超晶格的输运性质.结果表明,缺陷结构对纳米准周期链的电子输运性质有重要影响,特别是低能区电子输运 关键词： 缺陷 Fibonacci链 磁纳米结构 输运性质     

正方点阵上Fibonacci超元胞声子晶体的带结构

用平面波展开方法研究了水柱体作为填充物, 按照二维Fibonacci排列成超元胞填充在Hg基体中构成的声子晶体的声频带结构. 结果发现, 随着超元胞中准晶格常数的变化, 各个能带均出现三分裂. 对声场分布的研究发现了居间态的存在. 这些现象体现了准周期结构的特征. 关键词： Fibonacci排列 声子晶体 能带结构     

广义的一维Fibonacci结构

本文提出一维k组元的Fibonacci结构,它包含k个无公度的基本长度,是具有两个基本长度的标准Fibonacci结构的自然推广,投影理论被用来处理它的X射线衍射花样及其指标化问题,理论模拟被用于验证投影理论的结果,值得注意的是,对于有限的链长,当k足够大时,它的衍射谱将趋于混沌。 关键词：     

基于对称广义Fibonacci光子晶体结构的电光可调谐滤波器

本文构建了含有电光材料LiNbO3的一维对称广义Fibonacci光子晶体结构,提出并设计了一种基于该结构的可调谐滤波器,并利用传输矩阵法对设计的滤波器的可调谐滤波特性进行了理论研究.数据模拟结果表明:保持对称广义Fibonacci光子晶体的几何结构不变,通过改变电极所在处施加在电光介质(LiNbO3)层上的外加电场,...     

Fibonacci序列的统计属性和电子输运系数

对按膨胀规律A→AB和B→A生成的Fibonacci序列,采用一维随机行走模型数值计算了序列的自相关函数以及自行定义的准标准偏差.利用Hurst分析法研究了序列的再标度范围函数及其Hurst指数,并将结果与一维随机二元序列进行了对比.发现这些统计量有奇特的准周期振荡行为以及小于05的Hurst指数,直接论证了Fibonacci序列具有关联、标度不变及自相似等性质.从Anderson紧束缚模型出发,采用传输矩阵方法研究了Fibonacci序列的电子输运特性,讨论了输运系数对能量及其序列长度的依赖关系.研究 关键词： Fibonacci序列 统计属性 电子输运系数     

广义Fibonacci时间准周期量子行走波包扩散的动力学特性

本文通过数值计算的方法研究了一维离散时间准周期量子行走的动力学特性,主要研究了两个自旋空间C算符按照广义Fibonacci准周期排列的量子行走,发现对两类广义Fibonacci准周期序列,波包扩散都是超扩散(即标准方差σ约为t~γ,0.5γ1),而且在给定的两个C算符下,第二类广义Fibonacci准周期序列的幂指数γ大于第一类广义Fibonacci准周期序列.通过对波包扩散的概率分布情形和标准方差的研究发现,第一类广义Fibonacci准周期序列的波包扩散更接近于经典随机行走(γ=0.5),而第二类广义Fibonacci准周期序列的波包扩散更接近于均匀量子行走(γ=1),这与两类广义Fibonacci准周期量子自旋链中量子相变时的特性相反.     

Branching Rules and Gap-Labeling Properties for a Class of One-Dimensional Quasilattices

The gap-labeling properties of the energy spectrum for a dam of one-dimensional quasilatticeihave been investigated. We have studied the branching rules on subbands of the hierarchical energy sp&trum and obtained the integrated density of states (ZDOS). It is analytically
proved .that ZDOS has the form n + mα, where n and m are integers, α = √2 - 1. The daracteristic number m can be used to label the corresponding energy gap. This conclusion is similar to that of one-dimensional Fibonacci quasicrystals.     

Biphonons in quasicrystals

The spectrum of coupled optical biphonon vibrations in quasicrystals with variation of the atom-atom interaction in accordance with the Fibonacci sequence is investigated. For two-phonon states with strong anharmonicity of the vibrations, a system of recursion equations, which is more complicated than the previously employed system for one-phonon states, is obtained. Calculations using this system made it possible to determine the spectrum of biphonon vibrations in a quasicrystal. It is shown that, on the low-frequency edge of the biphonon band, a scaling-type fine structure of the same form as in biphonon spectra of fractal lattices exists in the density of states. It is found that the energy dependence of the density of states is periodic on a logarithmic scale. The period of this dependence is determined. It is noted that the resonance structure in the density of states is of a nonstandard form in the high-frequency region of the biphonon band. Fiz. Tverd. Tela (St. Petersburg) 39, 163–170 (January 1997)     

Trace maps as 3D reversible dynamical systems with an invariant

One link between the theory of quasicrystals and the theory of nonlinear dynamics is provided by the study of so-called trace maps. A subclass of them are mappings on a one-parameter family of 2D surfaces that foliate ³ (and also ³). They are derived from transfer matrix approaches to properties of 1D quasicrystals. In this article, we consider various dynamical properties of trace maps. We first discuss the Fibonacci trace map and give new results concerning boundedness of orbits on certain subfamilies of its invariant 2D surfaces. We highlight a particular surface where the motion is integrable and semiconjugate to an Anosov system (i.e., the mapping acts as a pseudo-Anosov map). We identify properties of symmetry and reversibility (time-reversal symmetry) in the Fibonacci trace map dynamics and discuss the consequences for the structure of periodic orbits. We show that a conservative period-boubling sequence can be identified when moving through the one-parameter family of 2D surfaces. By using generator trace maps, in terms of which all trace maps obtained from invertible two-letter substitution rules can be expressed, we show that many features of the Fibonacci trace map hold in general. The role of the Fricke character , its symmetry group, and reversibility for the Nielsen trace maps are described algebraically. Finally, we outline possible higher-dimensional generalizations.     

Purcell effect in one-dimensional photonic quasicrystals

The change in probability of spontaneous emission for emitter placed in one-dimensional photonic quasicrystal (optical Fibonacci lattice) was examined. When the dipole is placed in Fibonacci lattice two different scenarios can be expected: enhancing (if frequency and direction of the dipole emission correspond to optical eigenmode of structure, and position corresponds to maximum value of modes electric field profile) or suppression (in case of photonic band gap) of spontaneous emission rate. Fact that both effects are expressed in quasicrystals less than in the Bragg reflectors and in the microcavities was demonstrated.     

Fractal spectra in generalized Fibonacci one-dimensional magnonic quasicrystals

In this work we carry out a theoretical analysis of the spectra of magnons in quasiperiodic magnonic crystals arranged in accordance with generalized Fibonacci sequences in the exchange regime, by using a model based on a transfer-matrix method together random-phase approximation (RPA). The generalized Fibonacci sequences are characterized by an irrational parameter σ(p,q)$\sigma (p,q)$, which rules the physical properties of the system. We discussed the magnonic fractal spectra for first three generalizations, i.e., silver, bronze and nickel mean. By varying the generation number, we have found that the fragmentation process of allowed bands makes possible the emergence of new allowed magnonic bulk bands in spectra regions that were magnonic band gaps before, such as which occurs in doped semiconductor devices. This interesting property arises in one-dimensional magnonic quasicrystals fabricated in accordance to quasiperiodic sequences, without the need to introduce some deferent atomic layer or defect in the system. We also make a qualitative and quantitative investigations on these magnonic spectra by analyzing the distribution and magnitude of allowed bulk bands in function of the generalized Fibonacci number F_n and as well as how they scale as a function of the number of generations of the sequences, respectively.     

Optical Properties of Metal-Insulator Fibonacci Quasi-Periodic Superlattice

Based on the hydrodynamic theory and the transfer-matrix method, we have studied the optical properties by taking account of damping effects to the system of the metallic. and dielectric Fibonacci quasi-periodic superlattice for s-polarized soft x-rays and extreme ultraviolet. The analytical expression for the reflectivity is formally given. From our numerical results, we find that besides the reflection intensity spectrum has a very rich structure of self-similarity, the stronger reflection peaks appear at the region of soft x-rays and ultraviolet compared with metal-metal superlattice, and the width of the maxima is dependent on the dielectric functions of metallic and dielectric media. By using the periodic condition approximation, we also distussed the electromagnetic normal modes in the system, which explains the reflection spectra, and we found that with the increasing of the generation number, the electromagnetic modes all become localized.     

一族一维准晶的局部电子性质

本文利用推广的实空间重整化群方法,研究按膨胀规则(A,B)→(AⁿB,A)构造的一族一维泛Fibonacci准晶系(A_n序列)的局部电子性质。所引入的2n²+1种基本变换可计算该族一维准晶中任一A_n序列在任意格点的局部格林函数和局部态密度。结果表明,该方法是有效的,A_n链的电子局部态密度象Fibonacci准晶一样,呈现临界性。 关键词：     

Nonlinear Optical Response of a Fibonacci Multilayer

By studying numerically the light transmitting through a finite nonlinear Fibonacci multilayer, we find the gap-soliton-like phenomenon. The Fibonacci multilayer contains a Kerrtype nonlinearity in one component. When the frequency of incident light is in a stop gap, increasing the incident light intensity will make the system switch from a lower transmission state to a higher transmission state. Transmissivity for some frequencies can reach unit, which shows that they correspond to transparent states. Distribution of the field intensity in the Fibonacci structure has a particular gap-soliton-like shape, which has the multi-carrier wave.