共查询到15条相似文献,搜索用时 62 毫秒
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采用开轨道的量子谱函数,对二维圆环弹子球体系进行了量子谱分析,根据内环半径(f=Rin/Rout)的不同取值,分别计算了相应的量子谱函数的傅里叶变换谱.结果表明,量子峰的位置和粒子运动的经典轨道长度符合得很好,半经典的闭合轨道理论给予了很好的解释;但是随着内环半径的减小,尤其在内环的线度和de Broglie波长可比拟时,量子峰的性质发生了本质性的变化,其特征类似于光学中的衍射图样,这正是由于内环的衍射效应所引起的,非常符合具有波动性的Fresnel-Kirchhoff衍射定理.本文的计算为研究量子台球体系的动力学性质和微腔输运问题提供了理论基础,同时也为研究晶体衍射、光谱分析等提供了一种新的理论方法.
关键词:
圆环弹子球
量子谱函数
傅里叶变换
衍射效应 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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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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利用腔内量子电动力学效应改变钕玻璃微球荧光谱特性的研究 总被引:2,自引:1,他引:2
报道腔内量子电动力学效应对钕玻璃微球荧光谱的影响;分析了光谱中量子电动力学结构的相对强度,同时估算了自发辐射速率的量子电动力学增强。实验证实增强辐度超过16倍。 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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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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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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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
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J. S. Espinoza Ortiz M. A. M. de Aguiar A. M. Ozorio de Almeida 《Journal of statistical physics》1996,83(1-2):275-287
Compact billiards in phase space, or action billiards, are constructed by truncating the classical Hamiltonian in the action variables. The corresponding quantum mechanical system has a finite Hamiltonian matrix. In previous papers we defined the compact analog of common billiards, i.e., straight motion in phase space followed by specular reflections at the boundaries. Computation of their quantum energy spectra establishes that their properties are exactly those of common billiards: the short-range statistics follow the known universality classes depending on the regular or chaotic nature of the motion, while the long-range fluctuations are determined by the periodic orbits. In this work we show that the eigenfunctions also follow qualitatively the general characteristics of common billiards. In particular, we show that the low-lying levels can be classified according to their nodal lines as usual and that the high excited states present scars of several short periodic orbits. Moreover, since all the eigenstates of action billiards can be computed with great accuracy, Bogomolny's semiclassical formula for the scars can also be tested successfully. 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