共查询到17条相似文献,搜索用时 156 毫秒
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从Berry–Tabor求迹公式出发,导出了二维可积系统周期轨道作用量的半经典量子化条件.利用此量子化条件,考虑周期轨道满足的周期条件,得到了二维无关联四次振子系统周期轨道作用量的半经典量子化条件,并给出了半经典能级公式.对能级与周期轨道的对应关系做了分析. 相似文献
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研究了二维无关联四次振子系统,有理环面上积分 Hamiltonian运动方程给出了系统一系列周期轨道和经典物理量 ,使用半经典近似下的 Berry- Tabor求迹公式,得到了半经典的态密度.应用 Fourier变换分析了每条周期轨道对态密度的贡献,并与量子态密度的 Fourier变换结果比较证实了半经典求迹公式的有效性.Periodic orbits of two dimensional uncoupled quartic oscillator were calculated by inte grating Hamiltonian equations of motion on reasonable tori, and several classical quantities were also computed. Inserting them into Berry Tabor trace formula, a trace, i.e., the semiclassical density of states of the corresponding quantum system, was obtained. Finally, Fourier transform was adopted to verify the contribution of each periodic orbit. Good agreement between the semiclassical ... 相似文献
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从量子-经典轨道和几何相两方面, 研究了二维旋转平移谐振子系统的量子-经典对应. 通过广义规范变换得到了Lissajous经典周期轨道和Hannay角. 另外, 使用含时规范变换解析推导了旋转平移谐振子系统Schrödinger方程的本征波函数和Berry相, 得出结论: 原规范中的非绝热Berry相是经典Hannay角的-n倍. 最后, 使用SU(2)自旋相干态叠加, 构造一稳态波函数, 其波函数的概率云很好地局域于经典轨道上, 满足几何相位和经典轨道同时对应. 相似文献
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在有关偶数正多边形量子环对称连接特殊情形的自旋输运特性的研究基础上,进一步探讨了任意正多边形量子环的自旋输运性质.不仅解析地求解了相关电子散射问题,而且得到了 Landauer-Buttiker 电导的普遍公式,并讨论了它的圆环极限和 Aharonov-Casher 相位问题.结合数值计算,研究了正多边形量子环的Landauer-Buttiker 电导随多边形边数、引线连接方式、自旋轨道耦合强度以及电子波矢的周期变化特性和零点分布规律.
关键词:
Rashba 自旋-轨道耦合
Aharonov-Casher 相位
量子网络
量子输运 相似文献
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利用光纤中的量子几何相位(又称Berry相位),制作了单模光纤的线偏振光偏振面旋转器,并对器件进行了测量.实验数据表明,这种光纤偏振旋转器对光偏振面的旋转基本符合理论预计.对偏差进行处理后得到修正的定标公式,可更精确地反映出此光纤偏振旋转器的特性. 相似文献
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Sum rules are derived for the quantum wave functions of the Hadamard billiard in arbitrary dimensions. This billiard is a strongly chaotic (Anosov) system which consists of a point particle moving freely on a D-dimensional compact manifold (orbifold) of constant negative curvature. The sum rules express a general (two-point)correlation function of the quantum mechanical wave functions in terms of a sum over the orbits of the corresponding classical system. By taking the trace of the orbit sum rule or pre-trace formula, one obtains the Selberg trace formula. The sum rules are applied in two dimensions to a compact Riemann surface of genus two, and in three dimensions to the only non-arithmetic tetrahedron existing in hyperbolic 3-space. It is shown that the quantum wave functions can be computed from classical orbits. Conversely, we demonstrate that the structure of classical orbits can be extracted from the quantum mechanical energy levels and wave functions (inverse quantum chaology). 相似文献
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S. Gnutzmann P. Karageorge U. Smilansky 《The European physical journal. Special topics》2007,145(1):217-229
The sequence of nodal count is considered for
separable drums.
A recently derived trace formula for this
sequence stores geometrical information
of the drum. This statement is
demonstrated in detail
for the Laplace-Beltrami operator
on simple tori and surfaces of revolution.
The trace formula
expresses the cumulative sum of nodal counts
This sequence is expressed as
a sum of two parts:
a smooth (Weyl like) part which
depends on global geometrical
parameters, and a fluctuating part
which involves the classical
periodic orbits on the torus and
their actions (lengths). The geometrical
context of the nodal
sequence is thus explicitly revealed. 相似文献
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A. Richter 《Foundations of Physics》2001,31(2):327-354
Experimental tests of various trace formulas, which in general relate the density of states for a given quantum mechanical system to the properties of the periodic orbits of its classical counterpart, for spectra of superconducting microwave billiards of varying chaoticity are reviewed by way of examples. For a two-dimensional Bunimovich stadium billiard the application of Gutzwiller's trace formula is shown to yield correctly locations and strengths of the peaks in the Fourier transformed quantum spectrum in terms of the shortest unstable classical periodic orbits. Furthermore, in two-dimensional billiards of the Limaçon family the transition from regular to chaotic dynamics is studied in terms of a recently derived general trace formula by Ullmo, Grinberg and Tomsovic. Finally, some salient features of wave dynamical chaos in a fully chaotic three-dimensional Sinai microwave billiard are discussed. Here the reconstruction of the spectrum is not as straightforward as in the two-dimensional cases and a modified trace formula as suggested by Balian and Duplantier will have eventually to be applied. 相似文献
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Robert G. Littlejohn 《Journal of statistical physics》1992,68(1-2):7-50
The Van Vleck formula is an approximate, semiclassical expression for the quantum propagator. It is the starting point for the derivation of the Gutzwiller trace formula, and through this, a variety of other expansions representing eigenvalues, wave functions, and matrix elements in terms of classical periodic orbits. These are currently among the best and most promising theoretical tools for understanding the asymptotic behavior of quantum systems whose classical analogs are chaotic. Nevertheless, there are currently several questions remaining about the meaning and validity of the Van Vleck formula, such as those involving its behavior for long times. This article surveys an important aspect of the Van Vleck formula, namely, the relationship between it and phase space geometry, as revealed by Maslov's theory of wave asymptotics. The geometrical constructions involved are developed with a minimum of mathematical formalism. 相似文献
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A trace formula for the oscillating part of the level density for a spherical billiard has been obtained in spherical polar
coordinates. The Jacobian of stability and the length of the orbits are obtained from the classical mechanics of the problem.
The same formula is applicable to both the planar and the diametric orbits. Numerical results have been obtained with this
formula and compared with the results from exact quantum theory, EBK quantization, and Balian and Bloch. 相似文献
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We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier-transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classical method provides a bridge between quantum and classical mechanics. 相似文献