计及次近邻非谐相互作用下原子链中的非线性元激发

利用多重尺度法，研究了谐振、非谐的近邻和次近邻相互作用下单原子链的晶格振动行为， 发现非传播孤子在单原子链Brillouin区的任何位置均有可能存在.与仅考虑最近邻相互作用 下的单原子链的孤子群速相比，此时链中孤子的群速在Brillouin中央增大且衰减得更快； 在Brillouin区会出现另一个群速为零的位置.同时，孤子的幅度也相应增大且最大幅度孤子 的位置趋向于Brillouin中央. 关键词： 单原子链 非谐次近邻相互作用 非传播的孤子     

次近邻近似下具有在位势的一维双原子链中杂质引起的局域振动

考虑原子间次近邻相互作用,讨论了具有在位势的一维双原子链中杂质引起的局域振动,得到次近邻互作用力、在位势共同作用下局域模的存在条件及振动的基本特征.     

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.     

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．     

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.     

可集成量子计算中的非近邻相互作用

我们研究一维自旋1／2链中的非近邻相互作用的影响。和近邻相互作用相比，非近邻的相互作用强度一般会较弱，因而在以前的许多方案中，这种长程的相互作用被忽略了。本文首先估计由被忽略的非近邻相互作用所引起的量子逻辑门的误差。我们得到的结果是，这项误差不仅和非近邻相互作用的强度有关，更依赖于一维自旋链所包含的粒子数，忽略非近邻相互作用有可能会对可集成量子计算造成影响。我们进一步研究如何消除或者压缩这种长程的相互作用所造成的影响。我们提出了一个量子计算方案。在这种方案中，次近邻的相互作用的影响被完全消除，从而我们可以使量子逻辑门的精度得以提高。我们也讨论了这种方案在超导量子计算体系里面的物理实现问题。     

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.     

带有次近邻相互作用的非谐性线性链中亚声速和超声速孤子

基于相干态方法，在次近邻相互作用近似下研究了非谐性线性链中电子与声学晶格振动之间相互作用所引起的非线性效应，采用自治地处理运动方程的连续极限，立方非谐性形变势导致新的电子概率幅的非线性方程，并由此给出新的超椭圆积分形式的孤波解。证明除了通常的钟形孤子外，还存在另一种带有扭结状的孤波激发。 关键词：     

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.     

一维半导体高聚物中的激子态和发光性质及局部晶格畸变所产生的影响——Lancos严格对角化方法

应用Lanczos严格对角化方法在具有电子-电子强关联效应的情况下,研究一维高聚物半导体中激子态的能量和波函数的物性,并以此为基础计算了在有局部晶格畸变时激子态的变化及其对发光性质的影响.并发现在一定的互作用参数下,其发光强度与畸变的强度成正比关系. 关键词：     

Modulational Instability of Spinor Condensates in an Optical Lattice

We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.     

晶格振动对激子运动的影响

在本文中用Haga研究极化子时提出的微扰法讨论晶格振动对激子运动的影响。把作者过去的工作推广到电子和空穴质量不相等的普遍情形。在忽略反冲效应中不同波矢的声子之间的相互作用时,导出了激子的基态能量、有效质量、约化质量和内部势能。指出:激子的有效质量和电子、空穴与声子的相互作用有关;激子的约化质量不仅和电子、空穴与声子的相互作用有关,而且还和电子空穴质量比有关;激子形成自陷态的条件并非由电子、空穴与声子相互作用的大小,而是由电子、空穴质量比决定。形成激子自陷的条件是电子、空穴质量比0.261<μ_e/μ_h<3.83。在μ_e/μ_h<0.261或μ_e/μ_h>3.83的情形,激子极化晶体中并不形成自陷态。 关键词：     

The symmetries of wave equations on new lattices

This paper focuses on studying the symmetry of a practical wave equation on new lattices. It is a new step in that the new lattice equation is applied to reduce the discrete problem of motion of an elastic thin homogeneous bar. The equation of motion of the bar can be changed into a discrete wave equation. With the new lattice equation, the translational and scaling invariant, not only is the infinitesimal transformation given, but the symmetry and Lie algebras are also calculated. We also give a new form of invariant called the ratio invariant, which can reduce the process of the computing invariant with the characteristic equation.     

Amplification of light in one-dimensional vibrating metal photonic crystal

Photon–phonon interaction on the analogy of electron–phonon interaction is considered in one-dimensional metal photonic crystal. When lattice vibration is artificially introduced to the photonic crystal, a governing equation of electromagnetic field is derived. A simple model is numerically analyzed, and the following novel phenomena are found out. The lattice vibration generates the light of frequency which added the integral multiple of the vibration frequency to that of the incident wave and also amplifies the incident wave resonantly. On a resonance, the amplification factor increases very rapidly with the number of layers. Resonance frequencies change with the phases of lattice vibration. The amplification phenomenon is analytically discussed for low frequency of the lattice vibration and is confirmed by numerical works.     

On the tremendous effect of an electric field on the crystal lattice of quasi-one-dimensional conductors with a charge density wave

The deformation of the lattice of quasi-one-dimensional conductors with a charge density wave deformed by an electric field has been considered. In the case of the “strong” interaction between the charge density wave and lattice, the effect of the field can be compared to the usual piezoelectric effect with a tremendous piezoelectric modulus that is larger than the value in ionic crystals by a factor of L _c/λ (λ is the period of the charge density wave and L _c is the coherence length reaching several millimeters upon the sliding of the charge density wave). The interaction between the charge density wave and lattice is likely attributed to the possibility of the interband redistribution of charges (rearrangement of covalent bonds) in the process of the deformation of certain compounds with the charge density wave. The observed and expected effects provide a way of the creation of fundamentally new actuators including those of nanometer sizes.     

Observation of transverse instabilities in optically induced lattices

We study experimentally the Bloch-wave instabilities in optically induced photonic lattices. We reveal two different instability scenarios associated with either the transverse modulational instability of a single Bloch wave or the nonlinear interband coupling between different Bloch waves. We show that the transverse instability is greatly enhanced in the induced lattice in comparison with homogeneous media.     

Sound Wave of Spin-Orbit Coupled Bose-Einstein Condensates in Optical Lattice

We study the phonon mode excitation of spin-orbit(SO) coupled Bose-Einstein condensates trapped in a one-dimensional optical lattice. The sound speed of the system is obtained analytically. Softening of the phonon mode,i.e., the vanishing of sound speed, in the optical lattice is revealed. When the lattice is absent, the softening of phonon mode occurs only at the phase transition point, which is not influenced by the atomic interaction and Raman coupling when the SO coupling is strong. However, when the lattice is present, the softening of phonon modes can take place in a regime near the phase transition point. Particularly, the regime is widened as lattice strength and SO coupling increase or atomic interaction decreases. The suppression of sound speed by the lattice strongly depends on atomic interaction, Raman coupling, and SO coupling. Furthermore, we find that the sound speed in plane wave phase regime and zero-momentum phase regime behaves with very different characteristics as Raman coupling and SO coupling change. In zero-momentum phase regime, sound speed monotonically increases/decreases with Raman coupling/SO coupling, while in plane wave phase regime, sound speed can either increase or decrease with Raman coupling and SO coupling, which depends on atomic interaction.     

Frankel激子的有效质量与温度的关系

本文计及离子晶格的原子结构,用紧束缚方法导出了Frankel激子的有效质量与温度的关系。 关键词：     

环形腔中激光振荡输出的横向斑图及向光学湍流的转变

在研究环形腔中激光振荡输出的分岔与混沌的基础上,采用耦合映象格子模型研究了其空间扩展系统的横向效应.数值模拟表明,随着参数的改变,空间扩展系统由均匀稳态、行波解向时空混沌演化.在一定的参数条件下,空间扩展系统从光场取入射平面波(均匀分布)开始,经对称破缺向光学湍流转变. 关键词： 横向斑图 时空混沌 湍流 数值模拟