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Nechtschein等人报道并分析了反式聚乙炔中质子自旋晶格弛豫时间对拉摩频率ω和温度T的依赖关系。观察到了质子自旋晶格弛豫速率T1-1和ω-1/2的正比关系。但是在高频段,T1-1∝ω-1/2关系发生偏离,且温度越低,发生偏离的频率也越低。
本文用另一种方法对这些实验结果作了分析。首先,论证了孤子一维扩散模型的合理性。排除了质子弛豫速率∝ω-1/2的另一种解释,即仅仅是核自旋向着静止的顺磁中心扩散。孤子能处在运动状态或静止状态。当温度降低时,发生两个效应,即越来越少的孤子处于运动状态,且运动孤子的扩散系数减小。只有扩散的孤子对所观察到的质子弛豫有贡献,而固定孤子的贡献可以忽略。其次,描述了运动孤子的一维随机行走模型,计算了它的相关函数和谱密度函数。质子自旋晶格弛豫速率是:
其中C是运动孤子的浓度,τ是运动孤子沿链跳跃时,渡越相邻位置的跳跃时间,ω是质子的拉摩频率。
这个公式揭示了质子弛豫速率的频率和温度依赖关系的主要特征。它和Nechtschein的测量结果拟合得很好。从拟合中可以得到各个温度下运动孤子的跳跃时间和相对浓度。 相似文献
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利用单双激发多参考组态相互作用方法获得了LiAl分子基态X1∑+及七个激发态a3∏, A1∏, b3∑+, c3∑+, B1∏, C1∑+, d3∏的势能曲线, 通过势能曲线得到各态的平衡核间距Re, 进而求得绝热激发能和垂直激发能.计算结果表明:c3∑+ 电子态是一个不稳定的排斥态, A1∏态是一个较弱的束缚态, 其余6个电子态均为束缚态; b3∑+与 c3∑+态之间存在预解离现象; 8个电子态分别解离到两个通道, 即Li(2S)+Al(2P0)与Li(2P0)+Al(2P0). 接着将势能曲线拟合到Murrel-Sorbie解析势能函数形式, 据此获得各态的光谱数据:基态X1∑+的平衡键长为0.2863 nm, 谐振频率为316 cm-1, 解离能De为1.03 eV, 激发态a3∏, A1∏, b3∑+, c3∑+, B1∏, C1∑+, d3∏的垂直激发能依次为0.27, 0.83, 1.18, 1.14, 1.62, 1.81, 2.00 eV; 解离能依次为1.03, 0.82, 0.26, 排斥态, 1.54, 1.10, 0.93 eV, 相应谐振频率 ωe为339, 237, 394, 排斥态, 429, 192, 178 cm-1. 通过求解核运动的薛定谔方程找到了J=0时 LiAl分子7个束缚电子态的振动能级和转动惯量.
关键词:
LiAl
光谱常数
势能曲线
振动能级 相似文献
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基于一维分子晶体系统的 Holstein 模型,采用压缩-相干态展开方法,计及电子-声子间量子关联和重整化平移修正,分析和研究电子-双声子相互作用对极化子-孤子系统基态性质和量子涨落的影响.推导了一维极化子-孤子系统的封闭形式非线性方程.应用非线性项展开方法,给出非线性方程的解析解和相关基态特性结果.研究表明,仅当电子-双声子耦合强度 g1<0时非线性方程才有孤波解,此时声子量子涨落效应随着压缩的增加,极化子-孤子系统基态能量变得更负,孤子局域减少,孤子态更加稳定;另一方面,电子密度涨落〈Δ2n〉和声子坐标-动量的不确定量〈Δ2p〉〈Δ2q〉比无声子压缩效应的大,极化子结合能变得更负.特别是,当g1<0时,双声子效应的量子涨落〈Δ2n〉与〈Δ2p〉〈Δ2q〉的值比单声子情况有明显增加.
关键词:
压缩-相干态展开
极化子-孤子态与量子涨落
电子-双声子相互作用
非线性薛定谔方程 相似文献
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二维非定常Sine-Gordon方程辛算法及其孤子数值模拟 总被引:1,自引:1,他引:0
在矩形域[-a,a]×[-a,a]内对微分算子L=(ə2)/(əx2)+(ə2)/(əy2)用5点差分格式将二维非定常Sine Gordon方程离散化为一个2×7992阶非线性Hamilton系统.对该系统使用Euler中心格式,得到一个非线性方程组.对此方程组建立迭代解法并给出了这个迭代方法的收敛条件和收敛速度.Sine Gordon方程单孤子和双孤子的数值模拟试验显示该辛算法是有效的. 相似文献
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采用Davidson修正的内收缩多参考组态相互作用方法(MRCI+Q) 结合Dunning等的相关一致基aug-cc-pVnZ (n=D,T,Q,5,6) 计算了AlC分子X4∑-和B4∑-态的势能曲线, 并利用总能量外推公式将这两个态的总能量分别外推至完全基组极限. 对势能曲线进行核价相关修正及相对论修正, 并详细讨论了基组、核价相关和相对论修正 等对X4∑-和B4∑-电子态的能量和光谱常数的影响. 拟合核价相关及相对论效应修正的外推势能曲线, 得到了AlC分子X4∑- 和B4∑-电子态的主要光谱常数Te, Re, ωe, ωexe, ωeye, Be和αe. 它们与实验结果符合较好. 求解双原子分子核运动的径向Schrödinger方程, 找到了无转动的AlC分子两个电子态的全部振动态. 针对每一振动态, 还分别计算了其相应的振动能级和惯性转动常数等分子常数. 它们与已有的实验结果一致.
关键词:
光谱常数
分子常数
核价相关修正
相对论修正 相似文献
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利用定量相场模型, 以Mg-0.5 wt.%Al合金为例模拟了基面((0001)面)内镁基合金的等温自由枝晶生长过程. 通过研究该合金体系数值模拟的收敛性, 获得了最优化值耦合参数λ = 5.5及网格宽度Δx/W0 = 0.4, 并在该参数下系统研究了各向异性强度和过饱和度对枝晶尖端生长速度、尖端曲率半径、Péclet数及稳定性常数σ* 的影响. 结果表明, 由微观可解性理论得到的稳定性系数σ* 与ε6 拟合值σ*≅ ε6 1.81905, 更接近理想值σ * (ε6) ≅ε6 1.75. 此外, 当过饱和度Ω < 0.6时, 稳定性系数σ * 不随ε6 的变化而变化, 而当Ω > 0.6时, 稳定性系数σ * 随着ε6 的增加而减小. 这反映了枝晶的生长由扩散控制向动力学控制的转变. 随着过饱和度的增加, 枝晶形貌由雪花状枝晶向圆状枝晶转变. 相似文献
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R. Fedele H. Schamel 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,27(3):313-320
An investigation to deepen the connection between the family of nonlinear Schr?dinger equations and the one of Korteweg-de
Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis
for the current velocity, it is proven that the cubic nonlinear Schr?dinger equation, whose solution is a complex wave function,
can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the
latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the
current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schr?dinger equation,
starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current
velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant
current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily
large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u0 with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined
variable x-u0 s (s being a time-like variable). This novel method in solving the nonlinear Schr?dinger equation starting from the Korteweg-de
Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the
present paper and the ones already known in literature is also presented.
Received 20 February 2002 and Received in final form 22 April 2002 Published online 6 June 2002 相似文献
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Pang Xiao-feng 《Frontiers of Physics in China》2007,2(4):469-493
A new theory of bio-energy transport along protein molecules, where energy is released by the hydrolysis of adenosine triphosphate
(ATP), has recently been proposed for some physical and biological reasons. In this theory, Davydov’s Hamiltonian and wave
function of the systems are simultaneously improved and extended. A new interaction has been added into the original Hamiltonian.
The original wave function of the excitation state of single particles has been replaced by a new wave function of the two-quanta
quasi-coherent state. In such case, bio-energy is carried and transported by the new soliton along protein molecular chains.
The soliton is formed through the self-trapping of two excitons interacting with amino acid residues. The exciton is generated
by the vibration of amide-I (C=O stretching) arising from the energy of the hydrolysis of ATP. The properties of the soliton
are extensively studied by analytical methods and its lifetime for a wide range of parameter values relevant to protein molecules
is calculated using the nonlinear quantum perturbation theory. The life-time of the new soliton at the biological temperature
of 300 K is large enough and belongs to the order of 10−10 s or τ/τ
0 ⩾ 700. The different properties of the new soliton are further studied. The results show that the new soliton in the new
model is a better carrier of bio-energy transport and it can play an important role in biological processes. This model is
a candidate of the bio-energy transport mechanism in protein molecules.
相似文献
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In this paper, by using the bifurcation method of dynamical systems, we derive the traveling wave solutions of the nonlinear equation UUτyy ? UyUτy + U2Uτ + 3Uy = 0. Based on the relationship of the solutions between the Novikov equation and the nonlinear equation, we present the parametric representations of the smooth and nonsmooth soliton solutions for the Novikov equation with cubic nonlinearity. These solutions contain peaked soliton, smooth soliton, W-shaped soliton and periodic solutions. Our work extends some previous results. 相似文献
14.
G. A. Kotel’nikov 《Russian Physics Journal》2009,52(1):53-58
The kinematics of Cherenkov’s effect is considered for an electron moving in the Minkowski space with universal time and velocity
of light c = c
0 (1 + v
2/c
02)1/2, where c
0 = 3⋅10 m/s is the invariant constant and v is the particle velocity.
Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 47–50, January, 2009. 相似文献
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M. A. Krasil’nikov M. V. Kuzelev A. A. Rukhadze 《Journal of Experimental and Theoretical Physics》1997,85(4):705-711
A theoretical and numerical analysis is made of the dynamics of nonlinear electron-beam scattering of a wave reflected by
the emitting device of a plasma oscillator. It is shown that a counterpropagating plasma wave can interact nonlinearly with
other waveguide modes of the system and with charge-density beam waves, leading to changes in the operation of the oscillator.
It is established by means of a numerical simulation that the generation efficiency is reduced as a result of scattering of
the counterpropagating wave and stimulated emission of a strong-potential plasma wave with phase velocity v
ph=ω/k
z≪c.
Zh. éksp. Teor. Fiz. 112, 1299–1311 (October 1997) 相似文献
16.
The dynamics of the nonlinear excitations in a two-dimensional (2D) φ4-diatomic lattice, with nonlinear on-site electron-phonon coupling at the polarizable ion site has been presented, without
considering the self consistent phonon approximation. One of the major results obtained from our calculations is in the understanding
of continuous structural phase transition, where we have obtained the minimum in soft mode frequency at a soft mode temperatureT
s (>T
c), not at critical temperatureT
c. This occurs due to the anisotropy of such 2D systems. 相似文献
17.
S. Nazarenko 《JETP Letters》2006,83(5):198-200
I present a nonlinear differential equation model (DAM) for the spectrum of Kelvin waves on a thin vortex filament. This model
preserves the original scaling of the six-wave kinetic equation, its direct and inverse cascade solutions, as well as the
thermodynamic equilibrium spectra. Further, I extend DAM to include the effect of sound radiation by Kelvin waves. I show
that, because of the phonon radiation, the turbulence spectrum ends at a maximum frequency of ω* ∼ (ε3
c
s
20
/κ16)1/13, where ε is the total energy injection rate, c
s
is the speed of sound, and κ is the quantum of circulation.
The text was submitted by the author in English. 相似文献
18.
A theory is constructed for the dynamics and braking of domain walls in ferromagnets when a magnetic field is applied perpendicular
to the axis of easy magnetization (i.e., a transverse field H
⊥). The theory is valid for velocities v up to the limiting domain wall velocity v c. The Landau-Lifshitz equations in the dissipationless approximation are used to investigate the motion of domain walls and
the change in the character of the wall motion as its velocity v approaches v
c. The force acting on a domain wall due to viscous friction is calculated within the framework of generalized relaxation theory,
and the dependence of the domain wall velocity v on the forcing field H
z is investigated. Calculations of the braking force show that the contributions of various dissipation mechanisms to the friction
force have different dependences on the domain wall velocity, which affects the form of the function v=v(H
z). The shapes of the curves v(H
z) differ very markedly from one another for different values of the field H
⊥. The theory developed here can be used to describe the experimental results, in particular the almost linear behavior of
v=v(H
z) for small H
⊥ and its strongly nonlinear behavior when H
⊥∼H
a, whereas these data cannot be reconciled within the standard theory based on relaxation terms of Hilbert type.
Zh. éksp. Teor. Fiz. 112, 953–974 (September 1997) 相似文献