QUASIPERIODICITY OF TRANSCENDENTAL MEROMORPHIC FUNCTIONS

This paper is devoted to considering the quasiperiodicity of complex differential polynomials,complex difference polynomials and complex delay-differential polynomials of certain types,and to studying the similarities and differences of quasiperiodicity compared to the corresponding properties of periodicity.

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

We construct a one-dimensional quasiperiodic quantum walk to investigate the localization–delocalization transition.The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

Quantum phase transition and von Neumann entropy of quasiperiodic Hubbard chains

The half-filled Hubbard chains with the Fibonacci and Harper modulating site potentials are studied in a selfconsistent mean-field approximation. A new order parameter is introduced to describe a charge density order. We also calculate the von Neumann entropy of the ground state. The results show that the von Neumann entropy can identify a CDW/SDW （charge density wave/spin density wave） transition for quasiperiodic models.

Quantum diffusion in semi-infinite periodic and quasiperiodic systems

This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C（t） - t^-δ and d（t） - t^β. However, it finds that 0 〈δ 〈 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed.

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 fl-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.

Invariable mobility edge in a quasiperiodic lattice

We analytically and numerically study a 1 D tight-binding model with tunable incommensurate potentials.We utilize the self-dual relation to obtain the critical energy,namely,the mobility edge.Interestingly,we analytically demonstrate that this critical energy is a constant independent of strength of potentials.Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions,the inverse participation rate and the multifractal theory.All numerical results are in excellent agreement with the analytical results.Finally,we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.

Monte Carlo Simulation of the Potts Model on a Dodecagonal Quasiperiodic Structure

By means of a Monte Carlo simulation,we study the three-state Potts model on a two-dimensional quasiperiodic structure based on a dodecagonal cluster covering pattern.The critical temperature and exponents are obtained from finite-size scaling analysis.It is shown that the Potts model on the quasiperiodic lattice belongs to the same universal class as those on periodic ones.

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 non-Hermitian 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.

The Problem of Quasiperiodic Photonic Structures Solved by Considering the Cut of 2D Periodic Structure

The physical objective of solving for eigen-modes of a 1D quasiperiodic structure in photonics has been achieved. This was achieved thru considering this structure as a 1D projection or cut of a 2D periodic structure. And the problem is solved in a manner similar to 2D periodic photonic structures. A mechanical analogy (quasiperiodic orbits) helps to bring conceptual clarity.

Design and Optimization of Omnidirectional Band Gap for One-Dimensional Periodic and Quasiperiodic Phononic Heterostructures

A new kind of one-dimensional multilayer phononie heterostructure is constructed to obtain a broad acoustic omnidirectional reflection （ODR） band. The heterostructure is formed by combining finite periodic phononic crystals （PnCs） and Fibonacci （or Thue-Morse） quasiperiodic PnCs. From the numerical results performed by the transfer matrix method, it is found that the ODR bands can be enlarged obviously by using the combination of periodic and quasi-periodic PnCs. Moreover, an application of particle swarm optimization in designing and optimizing acoustic ODR bands is reported. With regards to different thickness ratios and periodic numbers in the heterostructure, we give some optimization examples and finally achieve phononic heterostructure with a very broad ODR bandwidth. The result provides a new approach to achieve broad acoustic ODR bandwidth, and will be applied in design of omnidirectional acoustic mirrors.

KAM-type Theorem for Nearly Integrable Hamiltonian with a Quasiperiodic Perturbation

In this paper we consider the persistence of invariant tori of an integrable Hamiltonian system with a quasiperiodic perturbation. It is proved that if the unperturbed system satisfies the Rtissmann non-degenerate condition and the perturbed system satisfies the co-linked non-resonant condition, then the majority of invariant tori is persistent under the perturbation.

Subdiffusion of Dipolar Gas in One-Dimensional Quasiperiodic Potentials

Considering the discrete nonlinear Schrodinger model with dipole-dipole interactions （DDIs）, we comparatively and numerically study the effects of contact interaction, DDI and disorder on the properties of diffusion of dipolar condensate in one-dimensional quasi-periodic potentials. Due to the coupled effects of the contact interaction and the DDI, some new and interesting mechanisms are found： both the DDI and the contact interaction can destroy localization and lead to a subdiffusive growth of the second moment of the wave packet. However, compared with the contact interaction, the effect of DDI on the subdiffusion is stronger. Furthermore and interestingly, we find that when the contact interaction （λ1） and DDI （A2） satisfy λ1 ≥ 2λ2, the property of the subdiffusion depends only on contact interaction; when λ1 ≤ 2λ2, the property of the subdiffusion is completely determined by DDI. Remarkably, we numerically give the critical value of disorder strength v＊ for different values of contact interaction and DDI. When the disorder strength v ≥ v＊, the wave packet is localized. On the contrary, when the disorder strength v ≤ v＊, the wave packet is subdiffusive.

Phase induced localization transition

Localization phenomenon is an important research field in condensed matter physics.However,due to the complexity and subtlety of disordered systems,new localization phenomena always emerge unexpectedly.For example,it is generally believed that the phase of the hopping term does not affect the localization properties of the system,so the calculation of the phase is often ignored in the study of localization.Here,we introduce a quasiperiodic model and demonstrate that the phase change of the hopping term can significantly alter the localization properties of the system through detailed numerical simulations,such as the inverse participation ratio and multifractal analysis.This phase-induced localization transition provides valuable information for the study of localization physics.

Real eigenvalues determined by recursion of eigenstates

Quantum physics is primarily concerned with real eigenvalues,stemming from the unitarity of time evolutions.With the introduction of PT symmetry,a widely accepted consensus is that,even if the Hamiltonian of the system is not Hermitian,the eigenvalues can still be purely real under specific symmetry.Hence,great enthusiasm has been devoted to exploring the eigenvalue problem of non-Hermitian systems.In this work,from a distinct perspective,we demonstrate that real eigenvalues can also emerge under the appropriate recursive condition of eigenstates.Consequently,our findings provide another path to extract the real energy spectrum of non-Hermitian systems,which guarantees the conservation of probability and stimulates future experimental observations.

一维准周期镶嵌模型的扩展态

最近的理论研究发现,一维准周期镶嵌模型存在迁移率边。在该文中,研究该模型的量子输运,尤其是扩展态的两端口电导,模型的输运相图、平均值和统计分布。扩展态的电导并不恒为1,而是有干涉共振条纹,用波函数的行为解释这些干涉条纹。该模型的扩展态能在极强的准周期势能下存活,通过电导的统计分布,以及与波函数分形维度的比较,解释其中的物理图像。

亚氯酸盐-硫代硫酸盐非缓冲体系的动力学

研究了亚氯酸盐-硫代硫酸盐反应体系在非缓冲条件下的复杂动力学行为.结果发现,在开放体系中反应的pH值和Pt电位存在准周期振荡分叉和混合模式振荡分叉通向混沌的过程,且pH峰与Pt电位峰反相位.当[ClO2-]与[S2O32-]起始浓度比相对较小时,随着流速的逐渐升高,体系的pH值和Pt电位从简单的小振幅振荡(S)经过准周期振荡分叉到混沌,最后回到简单大振幅振荡(L);而当[ClO2-]与[S2O32-]起始浓度比相对较高时,随着流速的降低,体系的pH值和Pt电位出现LS1、LS2、LS3…LSn的混合模式振荡,并在每对(LSn、LSn+1)振荡区间发现了LSn、LSn+1随机出现的非周期振荡行为.运用硫价态变化的一般动力学模型,模拟出了反应体系的混合模式振荡及非周期振荡.

滞环电流模式控制uk变换器的非线性现象研究

根据滑模变结构系统的原理,对滞环电流模式控制?uk 变换器的运行状态进行了研究。推导出在切换面上的等效控制,并导出了切换面上滑模运动的状态方程,以此状态方程为基础,可由特征值法来判断平衡点的稳定性。由特征值的数值计算结果证明,当参考电流增加时平衡点的失稳过程是超临界霍普分叉过程,各电路参数对参考电流的分叉点有重要影响。此外,数值仿真和电路实验均表明,滞环电流模式控制 ?uk 变换器的动态行为十分复杂,除周期态和极限环外,还可能产生准周期和混沌状态。这研究方法还可以推广到其它滑模控制非线性系统的研究中去。

悬臂输流管道的运动分岔现象和混沌运动

研究受约束悬臂输流管道的稳定性和运动分岔问题.在静态与动态失稳区域边界上的一个交叉点附近,用理论分析的方法详细研究了该系统可能发生的复杂运动和运动分岔现象.在动态失稳区域内发现了输流管道的概周期运动和由于概周期运动环面破裂而导致混沌的现象.理论分析结果与数值模拟结果相吻合.

裂纹转子的分岔与混沌特性分析

本文用数值方法研究带裂纹Jeffcott转子的分岔与混沌振动特性。研究结果表明 ,当裂纹较深时 ,裂纹转子在参数共振转速附近存在丰富的周期、拟周期振动和混沌运动 ;裂纹转子振动进入混沌的途径主要通过二次Hopf分岔实现。这些结论 。

准周期结构一维光子晶体的带隙特性与滤波特性

研究了准周期结构一维光子晶体的带隙特性和滤波特性,对ZnS与MgF2和GaAs与AlAs两种电 介质组合的光子晶体在层厚不变、折射率递变和折射率不变、层厚递变以及层厚不变、折射率比递变三种情况 下的透射谱作了模拟计算,得到了带隙特性的变化规律,并指出了其在滤波中的应用。与周期结构光子晶体相 比,准周期结构光子晶体的透射谱发生移动,带隙宽度改变。