一维Klein-Gordon/Fermi-Pasta-Ulam混合原子链中非线性参数作用的研究

采用推广的旋转平面波近似对一维非线性Klein-Gordon/Fermi-Pasta-Ulam混合原子链的运动方程进行简化,数值求解得到该系统中存在的离散呼吸子解.研究了系统中各非线性参数对该振动模的直流、一阶简谐项和二阶简谐项三个分量的对称性的影响以及对系统中局域模的影响. 关键词： Klein-Gordon/Fermi-Pasta-Ulam混合原子链 推广的旋转平面波近似 离散呼吸子 对称性     

一维分子链中激子与声子的相互作用和呼吸子解

运用连续极限近似，求解声子与激子相互作用的运动方程，得到了简谐分子链和 非简谐分子链中晶格振动的孤子解，在考虑三次非简谐势的情况下，一维分子链晶格振动具 有扭结孤子解，在考虑具有四次非简谐势的情况下，得到一维分子链晶格振动具有呼吸子解 . 关键词： 一维分子链 激子 声子 孤子 呼吸子 非线性效应     

一般情况下一维三原子链的求解及其色散关系

求解一般情况下一维三原子链的色散关系,讨论恢复力系数对色散关系的影响规律.研究结果表明,一般情况下一维三原子链不同的原子间恢复力系数对各支格波的频率、频谱宽度以及频率禁带宽度的影响规律均表现出不同特点,可实现对频率禁带宽度的精细调节.本文的相关研究结果是对固体物理学基础理论的深入探讨,可为带通滤波器的工程设计提供理论指导.     

一维双原子链中杂质的局域振动

讨论了一维双原子链中杂质的局域振动，对杂质原子替代大原子和替代小原子的情况进行了分析，分别得到这两种情况下的高频模和隙模的频率。     

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.     

一般情况下一维双原子链的求解及其色散关系

本文在简谐近似下采用原胞法求解一般情况下的一维双原子链的格波解和色散关系,讨论原子链结构参数对其色散关系的影响以及原胞内原子的振动特点。研究结果表明,晶格常数一定的情况下一维双原子链的色散关系与近邻原子相对间距无关;在布里渊区中心,长声学支格波近似为连续的弹性介质波,而长光学支格波近似为原胞内原子相对振动而原胞质心不动的驻波;在近邻原子间距和恢复力系数均相等的情况下,在布里渊区边界处短声学支格波和短光学支格波分别近似为波节在小原子和大原子的驻波。本文相关内容可为固体物理教学提供优质教学素材。     

6Li费米原子气中的配对能隙

在超导体中，为了拆散一个库珀对，必须提供某种激发能，这一能量的下限即所谓能隙．超导能隙可以通过光电子能谱实验进行测量．^6Li原子其质子、中子和电子的总数是奇数q，因此属于费米原子．除非^6Li原子两两结成库珀对，它们不可能共同占据量子力学的基态，实现玻色一爱因斯坦凝聚(BEC)．     

原子质量对一维三原子链色散关系的影响

本文采用数值分析方法研究原胞中原子质量对一维三原子链色散关系的影响,建立了频谱宽度和频率禁带宽度随原子质量变化的基本规律.结果表明,在原胞内只有一个原子质量发生变化的情况下,声学波频谱宽度随任一原子质量的增加而减小,光学波的频谱宽度随小原子质量的增加而增大,随大原子质量的增加而减小;两个频率禁带均随小原子质量的增加而变...     

不同边界条件下一维双原子链的晶格振动

在自由边界条件和驻波边界条件下，讨论分析了一维双原子链晶格振动的振动模和色散关系，并与周期性边界条件下的结果进行了比较；明确了在不同边界条件下讨论实际原子链晶格振动的振动模和色散关系，其结果是相同的。     

Discrete gap breathers in a diatomic K2-K3-K4 chain with cubic nonlinearity

The discrete gap breathers （DGBs） in a one-dimensional diatomic chain with K2-K3-K4 potential are analysed. Using the local anharmonicity approximation, the analytical investigation has been implemented. The dependence of the central amplitude of the discrete gap breathers on the breather frequency and the localization parameter are calculated. With increasing breather frequency, the DGB amplitudes decrease. As a function of the localization parameter, the central amplitude exhibits bistability, corresponding to the two branches of the curve ω = ω（ζ）. With a nonzero cubic term, the HS mode of DGB profiles becomes weaker. With increasing K3, the HS mode of DGB profiles becomes weaker and a bit narrower. For the LS mode, with increasing K3, the central particle amplitude becomes larger, and the DGB profile becomes much sharper. But, as k3 increases further, the central particle amplitude of the LS mode becomes smaller.     

Periodic, quasiperiodic and chaotic discrete breathers in a parametrical driven two-dimensional discrete diatomic Klein--Gordon lattice

We study a two-dimensional (2D) diatomic lattice of anharmonic oscillators with only quartic nearest-neighbor interactions, in which discrete breathers (DBs) can be explicitly constructed by an exact separation of their time and space dependence. DBs can stably exist in the 2D discrete diatomic Klein--Gordon lattice with hard and soft on-site potentials. When a parametric driving term is introduced in the factor multiplying the harmonic part of the on-site potential of the system, we can obtain the stable quasiperiodic discrete breathers (QDBs) and chaotic discrete breathers (CDBs) by changing the amplitude of the driver. But the DBs and QDBs with symmetric and anti-symmetric profiles that are centered at a heavy atom are more stable than at a light atom, because the frequencies of the DBs and QDBs centered at a heavy atom are lower than those centered at a light atom.     

Discrete gap breathers in a two-dimensional diatomic face-centered square lattice

In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry's theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.     

不变本征算符方法求解含不同在位势的一维双原子链的色散关系

本文运用全量子化的不变本征算符方法, 求解了含有不同简谐在位势的一维双原子链模型, 得到其色散关系并讨论了不同在位势系数之比和力常数对于色散关系高频支和低频支的影响, 分析发现在位势的存在使得低频支和高频支的频谱都有一定程度的抬高; 在一定的条件下, 布里渊区边界的高频支与低频支存在交点, 意味着在某些在位势下, 高频支与低频支的频隙为零. 关键词： 在位势 一维双原子链 不变本征算符方法 色散关系     

具有在位势的一维双原子链晶格振动的色散关系

在简谐近似下,求解具有在位势的一维双原子链晶格振动运动方程,得到了具有在位势的晶格振动的色散关系.在位势使色散关系声频支在布里渊区中心的振动频率不再为零,并且随在位势的增大而增大.对于原子之间相互作用势不随在位势大小变化的情况下,晶格振动的色散关系的频隙随在位势的增大而变宽.讨论了原子链由只有在位势的不连续极限(AC极限),通过在位势逐渐减弱而原子间相互作用势逐渐增强,最后演变到只有原子间相互作用势的原子链的情况.随着在位势减弱和相互作用势增强,色散关系的频隙由AC极限的孤立轻、重原子简谐振动频率之差逐渐变化到通常的无在位势的色散关系频隙.     

Interaction of phonons with discrete breathers in one-dimensional chain with tunable type of anharmonicity

In this paper, we consider the interaction of small amplitude waves (phonons) with standing discrete breather (DB) in the one-dimensional chain of harmonically coupled particles interacting with the anharmonic one-site potential, which can be of hard-type or soft-type anharmonicity. The coefficients of phonon reflection and transmission are calculated numerically. It is found that for the case of hard-type anharmonicity (soft-type anharmonicity) DBs are more transparent for short-wavelength (long-wavelength) phonon waves, while they efficiently reflect long-wavelength (short-wavelength) phonons. In thermal equilibrium, when all phonons have equal energy density, it is found that for the same width of the transparency window, DB transmits less energy in the case of the hard-type anharmonicity. This is so because, in this case, DB reflects long-wavelength phonons, which have larger group velocity and hence greater contribution to the net energy flux through the DB. In this sense, DBs more efficiently suppress thermal conductivity in the chain with hard-type anharmonicity. Our results contribute to a better understanding of the role of discrete breathers in the heat flow in nonlinear chains.     

在位势对于一维双原子链晶格振动长声学波的影响

根据声学模的定义,明确了具有在位势的一维双原子链的晶格振动不存在声学模,讨论了具有在位势的一维双原子链晶格振动的低频支长波模振动图像,得到原胞中两种原子运动的振幅不再一致,低频支长波模不再是原胞质心的运动,且两种原子运动的振幅比随在位势的增大而单调增大.     

Ferroelectricity in diatomic Ising chain as investigated by elastic Ising model

An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca₃CoMnO₆, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca₃Co_2-xMn_xO₆ (x ≈0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.