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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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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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近几年,量子台球问题引起人们的广泛兴趣.以前有很多对二维量子台球做过研究,相对于二维台球来说,三维台球更接近实际体系.本文以三维正方体量子台球为例,利用半经典闭合轨道理论计算了正方体量子台球中的经典开轨道,并研究量子谱函数与经典轨道长度之间的对应关系,发现他们之间对应的很好.这将有助于我们分析开放型量子台球中输运性质问题.利用这种方法物理图像清晰,计算量小并且可以帮助理解一些混沌体系的性质.这是半经典理论为联系量子力学与经典力学起桥梁作用的又一证明. 相似文献
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We use a semiclassical approximation to study the transport through the weakly open chaotic Sinai quantum billiards which can be considered as the schematic of a Sinai mesoscopic device,with the diffractive scatterings at the lead openings taken into account.The conductance of the ballistic microstructure which displays universal fluctuations due to quantum interference of electrons can be calculated by Landauer formula as a function of the electron Fermi wave number,and the transmission amplitude can be expressed as the sum over all classical paths connecting the entrance and the exit leads.For the Sinai billiards,the path sum leads to an excellent numerical agreement between the peak positions of power spectrum of the transmission amplitude and the corresponding lengths of the classical trajectories,which demonstrates a good agreement between the quantum theory and the semiclassical theory. 相似文献
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The fractal structure in the Rydberg lithium atoms in ionization dynamics of a static electric field 下载免费PDF全文
The ionization rate of Rydberg lithium atoms in a static electric field is examined within semiclassical theory which involves scattering effects off the core. By semiclassical analysis, this ionization process can be considered as the promoted valence electrons escaping through the Stark saddle point into the ionization channels. The resulting escape spectrum of the ejected electrons demonstrates a remarkable irregular electron pulse train in time-dependence and a complicated nesting structure with respect to the initial launching angles. Based on the Poincaré} map and homoclinic tangle approach, the chaotic behaviour along with its corresponding fractal self-similar structure of the ionization spectra are analysed in detail. Our work is significant for understanding the quantum-classical correspondence. 相似文献
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利用散射矩阵理论,结合扩展的半经典闭合轨道理论和多通道量子亏损理论,计算了磁场中高里德堡H2分子的回归谱.该方法使用了两个空间散射矩阵来描述里德堡电子的动力学性质,计算中可以包括所有阶的实散射的作用.回归谱的每一个尖峰对应着一条闭合轨道,新的额外峰是由于弹性散射和非弹性散射所引起的通道内和通道间的轨道组合,进一步证明了体系通道间和通道内的散射具有同等的重要性. 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