共查询到19条相似文献,搜索用时 234 毫秒
1.
采用近来提出的量子谱函数,我们把闭合轨道理论应用到半圆和四分之一圆弹子球系统,这种量子谱函数的傅利叶变换包含了连接任意两点的许多经典轨道的信息.计算表明量子谱的傅立叶变换和经典轨道的长度符合的很好.从这两个体系可以看出半经典理论为经典和量子力学提供了很好的桥梁作用. 相似文献
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利用SU(2)相干态的表示,我们构造了二维矩形弹子球中与经典周期轨道对应的波函数.经典周期轨道和量子波函数之间的关系可以通过物理图像清晰的表示出来.另外,利用周期轨道理论,我们计算了二维矩形弹子球体系的量子谱的傅立叶变换ρ(L).变换谱|ρN(L)|2对L图像中的峰可以和粒子在二维矩形腔中运动的经典轨迹的长度相比较.量子谱中的每一条峰正好对应一条经典周期轨道的长度,表明量子力学和经典力学的对应关系. 相似文献
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研究了二维椭圆台球中的量子谱和经典轨道之间的对应关系.为尝试求解没有解析波函数和本征能量又不能分离变量的体系,采用了定态展开方法(expansion method for stationary states,简称EMSS)得到尽可能精确的数值解,这是闭合轨道理论被推广到计算开轨道的情况.比较了傅里叶变换谱和经典轨道,发现量子谱的峰位置与经典轨道的长度在可分辨的范围内符合得很好,这是半经典理论为经典与量子力学的联系提供桥梁作用的又一个例子.
关键词:
椭圆量子台球
定态展开方法
闭合轨道理论
量子谱 相似文献
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矩形弹子球中的量子波包分析(英文) 总被引:1,自引:0,他引:1
利用波包分析量子力学体系的动力学行为在研究经典和量子的对应关系方面越来越成为一个非常重要的方法.利用高斯波包分析方法,我们计算了矩形弹子球体系的自关联函数,自关联函数的峰和经典周期轨道的周期符合的很好,这表明经典周期轨道的周期可以通过含时的量子波包方法产生.我们还讨论了矩形弹子球的波包回归和波包的部分回归,计算结果表明在每一个回归时间,波包出现精确的回归.对于动量为零的波包,初始位置在弹子球内部的特殊对称点处,出现一些时间比较短的附加的回归. 相似文献
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研究了二维Sinai台球系统的经典与量子的对应关系,运用定态展开法和Gutzwiller的周期轨道理论对Sinai台球系统的态密度经傅里叶变换得到的量子长度谱进行分析,并把量子长度谱中峰的位置与其所对应的经典体系的周期轨道长度做对比,发现两者之间存在很好的对应关系.观察到了一些量子态局域在短周期轨道附近形成量子scarred态或量子superscarred态.还研究了同心与非同心Sinai台球系统的能级最近邻间距分布,发现同心Sinai台球系统是近可积的,非同心Sinai台球系统在θ=3π/8下,随两中心间距离的增加,能级最近邻间距分布将由近可积向维格那分布过渡. 相似文献
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本文讨论正方形量子台球的输运性质,考虑电子以费米能量穿过台球区域,在台球出口和入口处对入射和出射波函数采用基尔霍夫散射.采用微扰论的Dyson方程得到半经典格林函数,并把赝路径半经典近似作微扰展开得到体系的传输矩阵元.比较了传输矩阵元的傅立叶变换谱的峰位置与腔内自由电子经典轨道长度,发现在精度允许范围内它们符合的很好. 相似文献
9.
本文讨论正方形量子台球的输运性质,考虑电子以费米能量穿过台球区域,在台球出口和入口处对入射和出射波函数采用基尔霍夫散射.采用微扰论的Dyson方程得到半经典格林函数,并把赝路径半经典近似作微扰展开得到体系的传输矩阵元.比较了传输矩阵元的傅立叶变换谱的峰位置与腔内自由电子经典轨道长度,发现在精度允许范围内它们符合的很好. 相似文献
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Wisniacki DA Vergini E 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》1999,59(6):6579-6584
The quantum dynamics of a chaotic billiard with moving boundary is considered in this paper. We found a shape parameter Hamiltonian expansion, which enables us to obtain the spectrum of the deformed billiard for deformations so large as the characteristic wavelength. Then, for a specified time-dependent shape variation, the quantum dynamics of a particle inside the billiard is integrated directly. In particular, the dispersion of the energy is studied in the Bunimovich stadium billiard with oscillating boundary. The results showed that the distribution of energy spreads diffusively for the first oscillations of the boundary (=2Dt). We studied the diffusion constant D as a function of the boundary velocity and found differences with theoretical predictions based on random matrix theory. By extracting highly phase-space localized structures from the spectrum, previous differences were reduced significantly. This fact provides numerical evidence of the influence of phase-space localization on the quantum diffusion of a chaotic system. 相似文献
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Quantum billiards have attracted much interest in many fields. People have made a lot of researches on the two-dimensional (2D) billiard systems. Contrary to the 2D billiard, due to the complication of its classical periodic orbits, no one has studied the correspondence between the quantum spectra and the classical orbits of the three-dimensional (3D) billiards. Taking the cubic billiard as an example, using the periodic orbit theory, we find the periodic orbit of the cubic billiard and study the correspondence between the quantum spectra and the length of the classical orbits in 3D system. The Fourier transformed spectrum of this system has allowed direct comparison between peaks in such plot and the length of the periodic orbits, which verifies the correctness of the periodic orbit theory. This is another example showing that semiclassical method provides a bridge between quantum and classical mechanics. 相似文献
13.
Random billiards are billiard dynamical systems for which the reflection law giving the post-collision direction of a billiard particle as
a function of the pre-collision direction is specified by a Markov (scattering) operator P. Billiards with microstructure are random billiards whose Markov operator is derived from a “microscopic surface structure” on the boundary of the billiard
table. The microstructure in turn is defined in terms of what we call a billiard cellQ, the shape of which completely determines the operator P. This operator, defined on an appropriate Hilbert space, is bounded self-adjoint and, for the examples considered here, a
Hilbert-Schmidt operator. A central problem in the statistical theory of such random billiards is to relate the geometric
characteristics of Q and the spectrum of P. We show, for a particular family of billiard cell shapes parametrized by a scale invariant curvature K (Fig. 2), that the billiard Laplacian P−I is closely related to the ordinary spherical Laplacian, and indicate, by partly analytical and partly numerical means, how
this provides asymptotic information about the spectrum of P for small values of K. It is shown, in particular, that the second moment of scattering about the incidence angle closely approximates the spectral
gap of P. 相似文献
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V. S. Vinogradov T. N. Zavaritskaya G. Karczewski I. V. Kucherenko N. N. Mel’nik W. Zaleszczyk 《Physics of the Solid State》2010,52(8):1757-1762
The Raman scattering and luminescence spectra of Zn1 − x
Mn
x
Te (0 ≤ x ≤ 0.6) quantum wires have been investigated. The quantum wires have been grown by molecular-beam epitaxy on the (100)GaAs
substrate with Au used as a catalyst. The spectrum of optical phonons in ZnMnTe quantum wires varies with a variation in x in accordance with an intermediate (between one- and two-mode) type of transformation. The optical phonon spectrum has been
analyzed in terms of the microscopic theory. It has been demonstrated that the experimental data can be brought in accord
with the theory by properly modifying the calculated density of phonon states for ZnTe. The spatial confinement has been found
to affect the electronic states in Zn1 − x
Mn
x
Te quantum wires. 相似文献
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María Eliana Defonsi Lestard María Eugenia Tuttolomondo Derek A. Wann Heather E. Robertson David W. H. Rankin Aida Ben Altabef 《Journal of Raman spectroscopy : JRS》2010,41(10):1357-1368
The molecular structure and conformational properties of ethyl trifluoroacetate, CF3CO2CH2CH3, were determined in the gas phase by electron diffraction, and vibrational spectroscopy (IR and Raman). The experimental investigations were supplemented by ab initio (MP2) and DFT quantum chemical calculations at different levels of theory. Experimental and theoretical methods result in two structures with Cs (anti–anti) and C1 (anti–gauche) symmetries, the former being slightly more stable than the latter. The electron‐diffraction data are best fitted with a mixture of 56% anti–gauche and 44% anti–anti conformers. The conformational preference was also studied using the total energy scheme, and the natural bond orbital scheme. Also, the infrared spectra of CF3CO2CH2CH3 are reported for the gas, liquid and solid states, as is the Raman spectrum of the liquid. The comparison of experimental averaged IR spectra of Cs and C1 conformers provides evidence for the predicted conformations in the IR spectra. Harmonic vibrational wavenumbers and scaled force fields have been calculated for both conformers. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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Doppler limited laser optogalvanic (LOG) spectra are obtained by irradiating a bromine discharge with a cw dye laser. The
discrete bands of the Br2
B-X system appear superimposed on a strong continuum. The LOG spectrum is closely identical with the absorption/emission spectrum
of Br2. Some extra bands and assigned in theB-X system are also observed and their vibrational quantum number assignment is given. 相似文献
17.
Philippe A. Jacquet 《Journal of statistical physics》2009,134(4):709-748
We introduce a model for charge and heat transport based on the Landauer-Büttiker scattering approach. The system consists
of a chain of N quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are
coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical
distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions,
we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix
the boundary values (T
L,μ
L) and (T
R,μ
R), and adjust the parameters (T
i
,μ
i
), for i=1,…,N, so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to
expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the
distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system
and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm
and Fourier laws. 相似文献
18.
E. M. Ganapol’skii 《JETP Letters》2012,96(7):456-460
Signs of quantum chaos in the spectra of linear Hamiltonian systems including scattering billiards of various configurations with kinks of the lateral surface have been experimentally studied. A billiard with kinks of the lateral surface at which the second derivative is indefinite constitutes a scattering K system. As a result, the spectrum of such a billiard and the corresponding model resonator becomes chaotic and the distribution of spectral intervals is close to a Wigner distribution. The spectral rigidity curves have been measured for a model microwave cavity whose shape is similar to the scattering billiard with kinks of the lateral surface. It has been found that the characteristics of the chaotic spectrum, the distribution of the spectral intervals, and the spectral rigidity curves for billiards with kinks of the lateral boundary exhibit signs of quantum chaos. 相似文献
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M.A. DoncheskiR.W. Robinett 《Annals of Physics》2002,299(2):208-227
Using the fact that the energy eigenstates of the equilateral triangle infinite well (or billiard) are available in closed form, we examine the connections between the energy eigenvalue spectrum and the classical closed paths in this geometry, using both periodic orbit theory and the short-term semi-classical behavior of wave packets. We also discuss wave packet revivals and show that there are exact revivals, for all wave packets, at times given by Trev=9μa2/4?π where a and μ are the length of one side and the mass of the point particle, respectively. We find additional cases of exact revivals with shorter revival times for zero-momentum wave packets initially located at special symmetry points inside the billiard. Finally, we discuss simple variations on the equilateral (60°-60°-60°) triangle, such as the half equilateral (30°-60°-90°) triangle and other “foldings,” which have related energy spectra and revival structures. 相似文献