混合准周期异质结构的带隙补偿与展宽

基于一维光子晶体异质结构的多帯隙交叠补偿思想,提出了一种新颖的混合准周期级联结构,用于扩大全方位光子带隙.该全方位反射器结构由Fibonacci准周期结构和Thue-Morse准周期结构级联构成,研究表明,相比单种准周期结构,其全方位光子带隙宽度有显著提高.系统研究了结构参数(如周期数、阶数、介质折射率和厚度)对该结构光子带隙的影响,通过与周期结构带隙特性的比较,分析了准周期结构易于实现多带隙交叠的原因,为更复杂带隙结构的补偿和展宽奠定了设计基础.     

Ising model in a quasiperiodic transverse field,percolation, and contact processes in quasiperiodic environments

Quantum Ising models in a transverse field are related to continuous-time percolation processes whose oriented percolation versions are contact processes. We study such models in the presence of quasiperiodic disorder and prove localization in the ground state, no percolation, and extinction, respectively, for sufficiently large disorder.     

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.     

准周期对spin-Peierls模型中晶格畸变和能隙的影响

采用严格对角化方法和自洽方法，研究准周期相互作用对spin-Peierls模型中晶格畸变和能隙的影响.研究表明，引入准周期作用后，spin-Peierls模型中晶格畸变和能谱表现出准周期结构的自相似特性.另外，在弹性系数K取不同值时，随着准周期作用强度的增强，晶格畸变的平均值可能会增大、减小或先增大后减小，其对应的能隙也有相似的行为. 关键词： 准周期相互作用 spin-Peierls模型     

横场中非束缚类准周期伊辛链的赝临界点

本文系统地研究了有限尺寸下非束缚类准周期量子伊辛链在横场中的赝临界点的行为. 首先, 通过计算平均磁矩和协作参量, 发现这两个量的导数随着横场的变化都会出现两个清晰的峰. 这与束缚类伊辛链和无序伊辛链的结果明显不同. 其次, 研究了横场中赝临界点的概率分布情况, 发现概率分布并不是高斯型的. 这也与无序的结果不同. 最后, 分析了赝临界点产生的原因, 发现赝临界点是由非束缚类准周期伊辛链中的集团结构造成的.     

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with nonHermitian either uniform or staggered quasiperiodic potentials.We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones,which implies that the system has mobility edges.The localization transition is accompanied by the PT symmetry breaking transition.While if the non-Hermitian quasiperiodic disorder is staggered,we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis.Interestingly,some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters.The reentrant localization transitions are associated with the intermediate phases hosting mobility edges.Besides,we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives.More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum,inverse participation ratio,and normalized participation ratio.     

Continuity of the Lyapunov Exponent for Quasiperiodic Operators with Analytic Potential

We study regularity properties of the Lyapunov exponent L of one-frequency quasiperiodic operators with analytic potential, under no assumptions on the Diophantine class of the frequency. We prove joint continuity of L, in frequency and energy, at every irrational frequency.     

准周期调制下自旋1/2反铁磁XY模型中的晶格畸变行为

利用严格对角化方法研究了Thue-Morse准周期调制下 自旋1/2反铁磁XY模型中的晶格畸变行为. 结果显示: 系统中每个格点的晶格畸变幅度介于均匀分布和无序分布之间. 对于较弱的准周期调制, 调制强度的增加有利于晶格畸变的形成. 但是, 对于较强的准周期调制, 调制强度的增加则阻碍晶格畸变的形成. 此外, 系统低能谱的能隙也明显受到准周期调制的影响. 关键词： 晶格畸变 Thue-Morse序列 准周期调制     

Quasi-periodic solutions and asymptotic properties for the nonlocal Boussinesq equation

We construct the Hirota bilinear form of the nonlocal Boussinesq(nlBq) equation with four arbitrary constants for the first time. It is special because one arbitrary constant appears with a bilinear operator together in a product form. A straightforward method is presented to construct quasiperiodic wave solutions of the nl Bq equation in terms of Riemann theta functions. Due to the specific dispersion relation of the nl Bq equation, relations among the characteristic parameters are nonlinear, then the linear method does not work for them. We adopt the perturbation method to solve the nonlinear relations among parameters in the form of series. In fact, the coefficients of the governing equations are also in series form.The quasiperiodic wave solutions and soliton solutions are given. The relations between the periodic wave solutions and the soliton solutions have also been established and the asymptotic behaviors of the quasiperiodic waves are analyzed by a limiting procedure.     

立方五次方非线性Schrodinger方程的动力学性质研究

采用辛算法数值求解了一维立方五次方非线性Schrödinger方程,研究了不同非线性参数下非线性Schrödinger方程的动力学性质.数值结果表明,随着立方非线性参数的增加,系统经历了拟周期状态、混沌状态和周期状态,且在五次方项的调制下,呼吸子解可以退化为单孤子解. 关键词： 非线性Schrödinger方程 动力学性质 孤子 辛算法     

Periodic,quasiperiodic, and chaotic breathers in two-dimensional discrete β-Fermi-Pasta-Ulam lattice

Using numerical method, we investigate whether periodic, quasiperiodic, and chaotic breathers are supported by the two-dimensional discrete Fermi-Pasta-Ulam (FPU) lattice with linear dispersion term. The spatial profile and time evolution of the two-dimensional discrete β -FPU lattice are segregated by the method of separation of variables, and the numerical simulations suggest that the discrete breathers (DBs) are supported by the system. By introducing a periodic interaction into the linear interaction between the atoms, we achieve the coupling of two incommensurate frequencies for a single DB, and the numerical simulations suggest that the quasiperiodic and chaotic breathers are supported by the system, too.     

The Landauer Resistivity on Quantum Wires

We study the Landauer resistivity of the Kronig–Penney model which has various behavior depending on the potential and the Fermi energy. In the case of the Sturmian quasiperiodic potential, we discuss examples in which lim inf of it is zero.     

Formation Mechanisms for the Spectral Characteristis of Low-Frequency Reverberations and Predictive Estimates

The paper considers the problem of monostatic scattering of low-frequency sound waves by nearsurface volumetric inhomogeneities under conditions of intense wind waves. We calculate the expected shape of the scattered signal spectrum taking into account the distribution of the volumetric inhomogeneities over the surface and their quasiperiodic motion in three-dimensional space under the action of wind waves. For deep-ocean conditions, a carrier frequency of 228 Hz, and a pulse duration longer than 100 s, we compare the experimental data on the shape of the reverberation spectrum with theoretical estimates. We compare the spectral levels of subsurface scattering with similar data on sound scattering directly on the wind-roughed surface.     

Models of Two-Level Atoms in Quasiperiodic External Fields

We prove that the spectrum of the generalized quasienergy operator of a plane-polarized two-level atom in a strong external quasiperiodic electromagnetic field with nonzero constant Fourier component is pure point, under Diophantine conditions on the frequency ratio, and excluding a small subset of resonant values. The widespread belief that there may be only pure point spectrum in such models is briefly discussed in Section 2 and the circularly polarized case—a well-known soluble model—is revisited from the point of view of the quasienergy operator..     

Optical Filters Using Optical Multi-Layer Structures for Optical Communication Systems

Abstract

In this article, light reflection spectrums for different one-dimensional multi-layer structures are obtained. Optical reflectivities for periodic, superperiodic, and quasiperiodic structures have been calculated using the transfer matrix method. PBGs of each structure have been obtained using the optical reflectivity pattern. From a comparison of reflectivity and standard dense wavelength division multiplexing grids, it is demonstrated that narrow and dense band filters can be built from generalized Fibonacci quasiperiodic structures. Reflectivity of these structures contains bands that meet the ITU-T dense wavelength division multiplexing standard. Reflectivity of other multi-layer structures has poor or less potential to be used in dense wavelength division multiplexing systems.     

On quantum stability for systems under quasiperiodic perturbations

We prove that the spectrum defined in terms of the autocorrelation function of a harmonic subject to a quasiperiodic perturbation, is, at resonance, transient absolutely continuous, covering the whole line. In the nonresonant case, and under some supplementary Diophantine condition, it is pure point, coinciding with the spectrum of a special almost-periodic function.     

The realistic QCD equation of state in relativistic heavy-ion collisions and the early Universe

The realistic equation of state of strongly interacting matter, that has been successfully applied in the recent hydrodynamic studies of hadron production in relativistic heavy-ion collisions at RHIC, is used in the Friedmann equation to determine the precise time evolution of thermodynamic parameters in the early Universe. A comparison with the results obtained with simple ideal-gas equations of state is made. The realistic equation of state describes a crossover rather than the first-order phase transition between the quark–gluon plasma and hadronic matter. Our numerical calculations show that small inhomogeneities of strongly interacting matter in the early Universe are moderately damped during such crossover.     

Elastohydrodynamic problems in quasicrystal elasticity theory and wave propagation

Elastohydrodynamic problems of decagonal quasicrystals are analysed where the phonon field obeys wave equation and the phason field obeys diffusive wave equation. Basic equations are solved in the quasiperiodic plane and periodic plane, respectively. Final governing equations of dynamic behaviours of decagonal quasicrystals are obtained. A general solution is derived in terms of introduced three auxiliary functions, where two individually satisfy a fourth-order partial differential equation and one satisfies a second-order hyperbolic diffusion equation. Using the derived governing equations, elastic waves propagating in the quasiperiodic plane and a plane containing the period axis are analysed. Secular equations are obtained. It is found that differing from conventional crystals, at least four branches of elastic waves exist when the phonon–phason coupling is present. Moreover, acoustic waves have attenuation during wave propagation. Phason fluctuations exhibit exponential decaying behaviour due to kinematic viscosity and damping. The phase speeds are isotropic in the quasiperiodic plane and anisotropic in a plane with the periodic axis. The section of the slowness surfaces is plotted.     

Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation

We show that the 1-dimensional Schrödinger equation with a quasiperiodic potential which is analytic on its hull admits a Floquet representation for almost every energyE in the upper part of the spectrum. We prove that the upper part of the spectrum is purely absolutely continuous and that, for a generic potential, it is a Cantor set. We also show that for a small potential these results extend to the whole spectrum.     

Brain stem neuronal noise and neocortical “resonance”

We present a qualitative model and data in evidence for the selection and stabilization of neocortical brain-wave power spectral modes by slow periodic and fast noise driving by brain stem neurons. Unlike noise effects in a bistable potential, increasing noise amplitude via more brain stem neurons increases the measure on unstable manifolds trapped in the saddle-sinks of the neural membrane attractor andincreases dwell times. We suggest that the effect of noise in expanding dynamical systems such as the generalized neuronal membrane equations studied here may be analogous to that of many-frequency quasiperiodic driving which leads to the stabilization of the EEG as a strange, nonchaotic attractor.