晶格振动色散关系与均匀杆纵振动色散关系的比较分析

一维单原子链晶格振动与均匀杆自由纵振动的运动方程在数学上存在内在的联系.将均匀杆自由纵振动运动方程中对空间的偏导数用差商代替,就得到一维单原子链晶格振动的运动方程.对于离散的一维单原子链晶格振动与连续的均匀杆自由纵振动的色散关系进行了比较分析.一维单原子链晶格振动的波矢具有特定的取值范围,即布里渊区,这是原子离散周期排布的结果.随着质量分布由离散逐渐向连续变化,一维单原子链晶格振动的色散关系逐渐演变为均匀杆纵振动的色散关系.     

考虑次近邻相互作用下一维单原子链中的孤立波

利用多重尺度法结合准不连续性近似,研究了涉及次近邻相互作用下的一维单原子链中的波动问题,得到了其新的色散关系.结果表明,在同时考虑次近邻相互作用和非谐相互作用的情况下,一维单原子链中不仅存在包络孤立波、扭状和反扭状孤立波,而且存在另一种孤立波形式的元激发——呼吸子. 关键词： 一维单原子链 非谐相互作用 孤立波     

一维三原子链的格波解及其色散关系

通过求解简谐近似下一维三原子链的晶格振动方程得到其格波解和色散关系,进而研究一维三原子链的晶格振动特点,讨论一维三原子链和一维单原子链色散关系的内在联系.结果表明,一维三原子链的色散关系包含一个声学支和两个光学支,频谱范围和频率禁带与原胞内三个原子的质量都有关联,在原胞内原子质量相等的情况下一维三原子链的色散关系与一维单原子链色散关系所描述的晶格振动模式相同,进而对固体物理教学中容易误解的两个相关问题进行了说明.     

一种制备单原子碳链的方案

考虑到迄今为止实验上尚不能制备含有上百个原子的自由单原子链,本文提出利用探针从graphene中拉伸较长单原子碳链的设想,并通过分子动力学计算发现,室温下可以利用C60探针以1 m/s的速度从graphene的zigzag边缘拉出较长的一维单原子碳链,为实验提供了一种制备单原子碳链的可能方案. 关键词： 碳链 一维 分子动力学 探针     

阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schrdinger方程,对方程进行解析求解.结果表明在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε2)级阻尼作用下,格孤波为钟状或扭结的孤子.     

一维j原子链晶格振动的色散关系

本文以一维j原子链晶格振动为理论计算模型,在简谐近似和最近邻近似下获得其晶格振动方程组,并分别令j=1, 2, 3得到了一维单原子、双原子以及三原子链晶格振动的色散关系,获得了与现有教材及文献中已有的相同结论.结果表明,本文所获得的一维j原子链晶格振动方程组具有一般性.紧接着以该组晶格振动方程组为出发点,通过数值模拟法分析原子间距、恢复力系数及原子质量等晶体结构参数对一维四原子链晶格振动色散关系的影响,进而加深了对固体物理学晶格振动相关内容的理解,并可为工程上带通滤波器的研发提供一定的参考.     

阻尼作用下一维非线性单原子链中的孤子

利用多重尺度法,研究了弱阻尼作用下一维非线性单原子链中的波动行为,发现在O(ε)级阻尼作用下其格波幅度减小,群速变慢.在晶格动力学中导出了参数耗散型非线性Schr?dinger方程,对方程进行解析求解.结果表明:在O(ε)级阻尼作用下一维非线性单原子链中的格孤波为传播的包络孤子;在O(ε²)级阻尼作用下,格孤波为钟状或扭结的孤子.     

纳米单原子链的热传导

根据Hardy能流密度公式、Kubo热导率公式,推导了纳米单原子链的热传导系数公式,并进行了数值计算.研究结果表明,纳米原子链的热传导系数小于无限长原子链的热传导系数,并且纳米原子链的长度越短,则热传导系数越小.这些现象可以作如下解释:原子链可以看作是一维晶格,格波在到达原子链端点时会发生反射,而改变了格波的能量传播方向,使能流密度降低,从而使纳米原子链的热导率小于无限长原子链的热导率.并且原子链越短,格波在到达原子链端点的过程中衰减越小,从而使反射格波的能流密度越接近于入射格波的能流密度,使能流密度更为降低,从而使纳米原子链的热导率更小.     

一维光子晶体斜入射波包的带隙结构

对波包的任意傅里叶分量进行坐标变换后,利用转移矩阵法推导出波包斜入射情形下一维光子晶体的色散关系表达式,利用色散关系曲线分析得出波包斜入射的第一带隙结构,与以往平面波的第一带隙结构不同,波包的带隙宽度小于平面波的带隙宽度,并且在位置上前者带隙包含在后者内部.比较了一维光子晶体分别在波包入射与平面波入射情形下带隙位置和宽度,分析了波包中心入射角的变化以及波包的角分布范围的变化对带隙结构的影响,得到了一维光子晶体对波包斜入射的带隙结构的基本特征,确定了计算波包带隙能够近似当作平面波处理的条件.研究表明,波包的带隙结构受入射角大小和波包角分布范围的影响.入射角越小,波包入射的带隙结构越接近平面波;波包的角分布范围越小,光子晶体对波包的带隙宽度和位置越接近平面波.     

一维光子晶体斜入射波包的带隙结构

对波包的任意傅里叶分量进行坐标变换后,利用转移矩阵法推导出波包斜入射情形下一维光子晶体的色散关系表达式,利用色散关系曲线分析得出波包斜入射的第一带隙结构,与以往平面波的第一带隙结构不同,波包的带隙宽度小于平面波的带隙宽度,并且在位置上前者带隙包含在后者内部.比较了一维光子晶体分别在波包入射与平面波入射情形下带隙位置和宽度,分析了波包中心入射角的变化以及波包的角分布范围的变化对带隙结构的影响,得到了一维光子晶体对波包斜入射的带隙结构的基本特征,确定了计算波包带隙能够近似当作平面波处理的条件.研究表明,波包的带隙结构受入射角大小和波包角分布范围的影响.入射角越小,波包入射的带隙结构越接近平面波;波包的角分布范围越小,光子晶体对波包的带隙宽度和位置越接近平面波.     

Propagation of General Wave Packets in Some Classical and Quantum Systems

In quantum mechanics the center of a wave packet is precisely defined as the center of probability. The center-of-probability velocity describes the entire motion of the wave packet. In classical physics there is no precise counterpart to the center-of-probability velocity of quantum mechanics, in spite of the fact that there exist in the literature at least eight different velocities for the electromagnetic wave. We propose a center-of-energy velocity to describe the entire motion of general wave packets in classical physical systems. It is a measurable quantity, and is well defined for both continuous and discrete systems. For electromagnetic wave packets it is a generalization of the velocity of energy transport. General wave packets in several classical systems are studied and the center-of-energy velocity is calculated and expressed in terms of the dispersion relation and the Fourier coefficients. These systems include string subject to an external force, monatomic chain and diatomic chain in one dimension, and classical Heisenberg model in one dimension. In most cases the center-of-energy velocity reduces to the group velocity for quasi-monochromatic wave packets. Thus it also appears to be the generalization of the group velocity. Wave packets of the relativistic Dirac equation are discussed briefly.     

Packet waves in a reaction-diffusion system

The finite-wavelength instability gives rise to a new type of wave in reaction-diffusion systems: packet waves, which propagate only within a wave packet, are found in experiments on the Belousov-Zhabotinsky reaction dispersed in water-in-oil AOT microemulsion (BZ-AOT) as well as in model simulations. Inwardly moving packet waves with negative curvature occur in experiments and in a model of the BZ-AOT system when the dispersion d omega(k)/dk is negative at the characteristic wave number k(0). This result sheds light on the origin of anti-spirals.     

Quantum dynamics of charge transfer on the one-dimensional lattice:Wave packet spreading and recurrence

The wave function temporal evolution on the one-dimensional(1D) lattice is considered in the tight-binding approximation. The lattice consists of N equal sites and one impurity site(donor). The donor differs from other lattice sites by the on-site electron energy E and the intersite coupling C. The moving wave packet is formed from the wave function initially localized on the donor. The exact solution for the wave packet velocity and the shape is derived at different values E and C. The velocity has the maximal possible group velocity v = 2. The wave packet width grows with time ～ t1/3and its amplitude decreases ～ t-1/3. The wave packet reflects multiply from the lattice ends. Analytical expressions for the wave packet front propagation and recurrence are in good agreement with numeric simulations.     

On the mass of a wave packet in plasma

The relativistic mass density which is transported by a quasi-monochromatic transverse wave packet is derived. The wave packet is assumed to propagate in isotropic cold collisionless plasma. The co-ordinate frame moving with the group velocity appears as the rest frame for both the mass density and the total mass of the wave packet. The equivalence of the energy-mass relation and the dispersion equation is demonstrated.     

Nonadiabatic effects in the phonon spectrum of metal compounds

It is shown that nonadiabatic corrections to the dispersion law of optical phonons in the region of small wave vectors in the case of branches, for which the vibration with a zero wave vector is not accompanied by the appearance of a dipole moment in the ionic lattice, are significant for all possible directions of the wave vector. If a dipole moment arises, nonadiabatic corrections reach a noticeable value only for the wave-vector directions that are almost perpendicular to the direction of the dipole moment.     

Features of wave generation by a source moving along a one-dimensional flexible guide lying on an elastic-inertial foundation

A self-consistent dynamic problem is posed for a system including a one-dimensional flexible guide (a string), elastic-inertial foundation (an array of oscillators), and moving oscillating load. The effect of the foundation parameters on the dispersion characteristics (frequency, phase velocity, and group velocity as functions of the wavenumber) of transverse waves propagating along the string has been analyzed. It has been shown that taking into account the foundation inertia leads to the presence of two critical (cutoff) frequencies. Regularities of wave generation by a source moving along the string have been analyzed.     

On the velocity of propagation of a frequency-modulated wave packet in a dispersive absorbing medium

It is shown that the velocity of propagation of a frequency-modulated wave packet through a strongly dispersive absorbing medium can be significantly different from (either higher or lower than) that of a non-frequency-modulated wave packet. This difference is attributed to the absorption dispersion of the medium. The easiest way to take the absorption dispersion into account is to use the formalism of the complex group velocity of a wave packet. This paper considers the propagation of a linear frequency-modulated wave packet, whose carrier frequency is close to the frequency of a spectral absorption line of the medium.     

Phase velocities of plane waves in a pipe with a flow whose velocity varies along the radius

The phase velocities of plane waves in a pipe filled with a moving acoustic medium are studied for different laws of flow velocity variation along the pipe radius. The wave equation is solved by the discretization method, which breaks the entire pipe volume into individual cylinders under the assumption that, within each of the cylinders, the flow velocity of the medium is constant. This approach makes it possible to reduce the solution to the wave problem to solving Helmholtz equations for individual cylinders. Based on boundary conditions satisfied at the boundaries between neighboring cylinders, a homogeneous system of linear algebraic equations is obtained. From this system, with the use of the scattering matrices, a simple dispersion equation is derived for determining the phase velocities of plane waves. The stability of the numerical solution to the dispersion equation with respect to the number of cylinders is investigated. The phase velocities of quasi-homogeneous and inhomogeneous waves in a pipe are numerically calculated and analyzed for different velocities of a moving medium and different laws of flow velocity variation along the radius. It is shown that the variation that occurs in the phase velocity of a homogeneous plane wave in a pipe due to the motion of the medium is identical to the mean flow velocity for different laws of flow velocity variation along the radius. For inhomogeneous plane waves, the phase velocity increment exceeds the mean flow velocity several times and depends on both the law of wave amplitude distribution along the radius and the law of the flow velocity variation along the radius.