一维更键Heisenberg铁磁链间隙非线性元激发

对于一维更键铁磁链Heisenberg模型，在一级近似下：1）存在磁间隙孤子（振动频率位于磁频谱间隙内）和响应扭结（振动频率位于磁频谱内）；2）内禀局域模（振动频率位于所有磁频谱带上方）是不可能存在的． 关键词：     

具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模(英文)

基于Hartree-Fock方法和多标度方法,我们考察了具有格点各向异性的一维铁磁链中的量子孤子和内禀局域模,量子磁振子的波函数由量子包络孤子来描述.在布里渊区边界,量子包络孤子变成了量子内禀局域模,它的量子本征频率在简谐波带的顶部上方,量子磁振子主要集中在中心位置j=j0的附近.     

一维单原子链中杂质引起的局域振动模

讨论了一维单原子链中杂质引起的晶格局域振动模和局域振动图像,分析了杂质质量和杂质近邻力常数对振动模的影响,通过数值求解晶格振动运动方程组．给出了局域振动模关于杂质质量和杂质近邻力常数分布的相图;分析了含杂质晶格振动模频率相对于完整晶格振动模频率的变化。     

聚乙炔孤子的二维局域振动模及其键弯曲势的影响

本文考虑了反式聚乙炔的平面结构,在二维空间内研究了孤子的局域振动模,并在此基础上讨论了键弯曲势对孤子局域模的影响,结果发现:1)晶格在垂链方向的振幅与链向的可比拟;2)当耦合参数λ取定值时,产生新的局域模(与SSH模型比较),且局域模的数目随着键弯曲势参数K的增加而增多,其局域性也随之增强。 关键词：     

掺杂、无序和混晶半导体的晶格振动行为

一、研究的意义和目的 杂质诱发的半导体晶格振动问题和无序和混晶半导体的晶格振动问题的研究,在过去20多年中一直是比较活跃的. 过去的研究表明,在杂质诱发晶格振动情况下,由于杂质原子量和掺杂的不同而引起的力常数的变化,可以诱发与杂质有关的、不同程度局域化的振动模(尤其是位于声子带上方的局域模),并可使原来光学不激活的声子带模变得部分地光学可激活.然而对与低频的声学声子带有关的杂质诱发振动行为,国内外却研究得很少,实验方面尤其如此. 关于无序半导体的晶格振动行为,已有的研究成果表明,无序可以使理想晶体情况下光s学不激活…     

三元合金缺陷层对有限超晶格中局域界面光学声子模的影响

在宏观介电连续近似下，采用转移距阵方法，研究了三元合金缺陷层对有限超晶格中局域界面光学声子模的影响.在这种有限超晶格结构中，可以清楚地看到所有界面模的演化轨迹.结果表明：存在两类局域模，它们的宏观静电势波函数分别局域在缺陷层和表面层附近，且这些模随着超晶格组分层和缺陷层的相对厚度和介电常数的改变，其局域位置和特性发生显著变化.此外，发现虽然能隙中局域模的数目不守恒，但所有界面模的总数守恒.     

一维双原子链中杂质引起的局域振动模

对含杂质的一维双原子链,在链中所有原子之间近邻相互作用力常数均相等的情况下,数值求解晶格振动的运动方程组,得到不同局域振动模的振动图像和产生条件,给出了局域模关于杂质原子质量和原胞中两种晶格原子质量比分布的相图．     

具有在位势的一维双原子链中杂质引起的对称局域模

对具有在位势且含杂质的一维双原子链的晶格振动方程组进行求解,得到了局域振动的解析解,给出了在位势对局域振动影响的基本特征,并简要讨论了对称局域模的存在形式.     

两耦合半无限超晶格中的局域界面声子-极化激元

采用转移矩阵方法，研究了含结构缺陷层的两耦合半无限超晶格(GaAs/AlAs)中的局域界面声子-极化激元模性质. 研究发现，含不同介电特性的缺陷超晶格结构中的局域界面声子-极化激元模在剩余射线区［ω_TO, ω_LO］的分布情况与数量存在不同，而且反对称模表现出不同的特征. 文中着重研究了缺陷层介电常数与角频率无关的缺陷超晶格，发现该结构中的局域界面声子-极化激元模对组分层的排列顺序与厚度、缺陷层的厚度以及横向波数有着不同程度的依赖.     

磁性斯格明子晶格的磁弹现象与机理

近年来,人们在一些具有手性相互作用的磁性体材料及薄膜中成功观测到具有非平凡拓扑性质的二维自旋结构,称作磁性斯格明子.在大部分情况下,磁性斯格明子自发地聚集成一种晶格结构,称作斯格明子晶格.孤立的斯格明子由于其奇特的拓扑性质以及优异的电流驱动性质等"局域化特征"受到人们的广泛关注.与此相对,斯格明子晶格作为一种新颖的宏观磁性相,可能与材料固有的多场耦合性质发生相互作用进而引发许多奇特的宏观物理现象乃至新性质.在此范畴内,人们发现由于手征磁体内禀的磁弹耦合,斯格明子晶格不但对材料的力学性质产生影响,而且在外力作用下自身具备"层展的弹性性质".本文对相关现象进行梳理,并基于一种针对B20族手征磁体磁弹耦合效应普遍适用的热力学唯象模型,逐一简述对于不同类型的磁弹现象如何建模分析,进而给出其中一部分现象的实验与理论结果比对.最后,对这一领域的发展提出几个可供进一步探索的方向.     

Nonlinear nanoscale localization of magnetic excitations in atomic lattices

Reviewed here is the nonlinear intrinsic localization expected for large amplitude spin waves in a variety of magnetically ordered lattices. Both static and dynamic properties of intrinsic localized spin wave gap modes and resonant modes are surveyed in detail. The modulational instability of extended nonlinear spin waves is discussed as a mechanism for dynamical localization of spin waves in homogeneous magnetic lattices. The interest in this particular nonlinear dynamics area stems from the realization that some localized vibrations in perfectly periodic but nonintegrable lattices can be stabilized by lattice discreteness. However, in this rapidly growing area in nonlinear condensed matter research the experimental identification of intrinsic localized modes is yet to be demonstrated. To this end the study of spin lattice models has definite advantages over those previously presented for vibrational models both because of the importance of intrasite and intersite nonlinear interaction terms and because the dissipation of spin waves in magnetic materials is weak compared to that of lattice vibrations in crystals. Thus, both from the theoretical and the experimental points of view, nonlinear magnetic systems may provide more tractable candidates for the investigation of intrinsic localized modes which display nanoscale dimensions as well as for the future exploration of the quantum properties of such excitations.     

Localized vibrational modes in an <Emphasis Type="Italic">A</Emphasis><Subscript>3</Subscript><Emphasis Type="Italic">B</Emphasis> two-dimensional perfect crystal

The possibility of existence of nonlinear localized vibrational modes in an A₃B two-dimensional crystal with pairwise interatomic bonds is demonstrated. Such modes are easily realized when the difference between masses of atoms A and B is significant and the spectrum of small-amplitude crystal vibrations has a sufficiently wide gap. The influence of the uniform tension/compression deformation on the small-amplitude crystal vibration spectrum and on the existence of nonlinear localized modes is investigated. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 73–79, August, 2008.     

Intrinsic Localized Spin Wave Modes and Modulational Instability in a Two-Dimensional Heisenberg Ferromagnet

An analytical study on the properties of intrinsic localized modes and modulational instability in a quantum two-dimensional ferromagnet with single-ion uniaxial anisotropy is completed in the semiclassical limit. By making use of the semidiscrete multiple-scale method, we obtain a line localized solution and a radially symmetric localized solution, and analyze their existence conditions. Taking into account that the existence of bright localized solutions is closely linked to the modulational instability of plane waves, we analytically study the discrete modulational instability of plane spin waves. The result of the modulational instability analysis show that the uniaxial anisotropy plays a key role in the appearance of our intrinsic localized spin wave modes.     

Intrinsic localized modes in nonlinear photonic crystal waveguides

A discussion is given of the theory of intrinsic localized modes (ILM) for nonlinear waveguide impurities in photonic crystals. Conditions are determined for the existence of both even- and odd-parity ILM modes and kink ILM modes. A study is also made of ILM modes in a two-dimensional array of Kerr impurities.     

Intrinsic Localized Spin-Wave Modes in an Anisotropic Ferromagnet with Dzyaloshinsky-Moriya Interaction

The existence and properties of intrinsic localized spin-wave modes in a ferromagnetic XXZ spin chain with Dzyaloshinsky-Moriya interaction are investigated analytically in the semiclassical limit. The model Hamiltonian is quantized by introducing the Dyson-Maleev transformation and the coherent state representation is chosen as the basic representation of the system. By making use of the method of multiple scales combined with a quasidiscreteness approximation, the equation of motion for the coherent-state amplitude is reduced to the nonlinear Schrödinger equation. It is shown that a bright intrinsic localized spin-wave mode whose eigenfrequency lies below the bottom of the magnon frequency band can exist in the ferromagnetic system. We also show that the system can produce a dark intrinsic localized spin-wave mode, i.e., nonpropagating kink, whose eigenfrequency is below the upper of the magnon frequency band. In addition, we find that the introduction of the Dzyaloshinsky-Moriya interaction changes wave numbers in the Brillouin-zone corresponding to the appearance of intrinsic localized spin-wave modes.     

Solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain

By use of the Hartree approximation and the method of multiple scales, we investigate quantum solitons and intrinsic localized modes in a one-dimensional antiferromagnetic chain. It is shown that there exist solitons of two different quantum frequency bands: i.e., magnetic optical solitons and acoustic solitons. At the boundary of the Brillouin zone, these solitons become quantum intrinsic localized modes: their quantum eigenfrequencies are below the bottom of the harmonic optical frequency band and above the top of the harmonic acoustic frequency band.     

Free localized vibrations of a semi-infinite cylindrical shell

Free vibrations of a semi-infinite cylindrical shell, localized near the edge of the shell are investigated. The dynamic equations in the Kirchhoff-Love theory of shells are subjected to asymptotic analysis. Three types of localized vibrations, associated with bending, extensional, and super-low-frequency semi-membrane motions, are determined. A link between localized vibrations and Rayleigh-type bending and extensional waves, propagating along the edge, is established. Different boundary conditions on the edge are considered. It is shown that for bending and super-low-frequency vibrations the natural frequencies are real while for extensional vibrations they have asymptotically small imaginary parts. The latter corresponds to the radiation to infinity caused by coupling between extensional and bending modes.     

Discrete breathers in two-dimensional Josephson-junction arrays

We have proposed theoretically and studied numerically the existence of discrete breathers (intrinsic localized modes) in the dynamics of a two-dimensional Josephson-junction array biased by radio-frequency fields. The solutions are linearly stable in the framework of the Floquet theory and robust in the presence of thermal fluctuations. We have also discussed the conditions for realizing an experimental detection of these modes.     

Lokalisierte Schwingungszustände von Punktdefekten im einfach-kubischen Gitter

Frequencies of localized vibrations in a simple cubic lattice are discussed, using a simplified model with nearest neighbour interaction only. The modes are determined by group-theoretical considerations. The frequencies are given in terms of tabulated functions. A substitutional impurity and a vacancy can be described approximately by this model. It turns out that a vacancy does not show localized vibrations. An approximation method is discussed and compared with the exact results. It gives good results if the vibration is strongly localized, and it can easily be extended to other lattices.     

Lokalisierte Schwingungszustände in kubischen Kristallen mit Punktdefekten

The localized modes of vibration are discussed for a face centered and a body centered cubic lattice, if the ideal crystal is perturbated by a substitutional impurity. The eigenvectors are found by group-theoretical considerations, the frequencies can be calculated approximately by a variational principle, which gives good results, if the mode is strongly localized. It is discussed, which changes in mass and coupling parameters can give rise to localized modes of vibration. It turns out that in the model, which is considered here (nearest neighbour interaction and no changes in lattice structure), a vacancy does not show localized vibrations.