开放量子台球体系散射的赝路径半经典近似

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.     

开放量子台球体系散射的赝路径半经典近似

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．     

正方体量子台球的半经典分析(英文)

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.     

二维椭圆量子台球中的谱分析

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     

二维Sinai台球系统的量子混沌研究

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.     

斯托克斯矢量法在全光纤电流传感器中的应用

针对目前全光纤电流传感器中光信号检测环节多是采用双路光强分析偏振度这一现状,提出将斯托克斯矢量法应用于光纤电流传感器信号偏振度的演变分析,在近似条件下,推导得到基于穆勒矩阵的光纤电流传感器简化传输矩阵.从琼斯矢量法和实验结果的比较可知,斯托克斯矢量法与琼斯矢量法的模拟效果十分接近,此外它还具有传输矩阵中不存在复数、容易简化为稀疏矩阵以及最终偏振度只需计算总传输矩阵的第2个对角元即可等运算优势.这些优势使得该方法不仅可以很好地进行理论分析,还可以有效地简化分析过程和运算过程.     

周期性层状结构材料中光子带隙的形成

结合经典电磁场理论和Bloch定理,讨论了光波在周期性层状结构材料中传播的色散关系,并通过传输矩阵方法得到光波的透射谱,指出在周期性层状结构中波阻抗是形成光子带隙的本质因素.     

Dirac方程中的量子与经典对应

根据Heisenberg对应原理(HCP),在经典极限下厄密算符的量子矩阵元对应经典物理量的Fourier展开系数.将HCP应用到相对论领域的Dirac方程中,对于自由粒子和在匀磁场中的带电粒子,其量子算符的矩阵元在经典极限下对应着相对论物理方程的解.计算表明,在经典极限下量子期望值就是对应经典物理量的时间平均值.     

偏振光大气传输的前向散射新模型

建立了偏振光空间传输前向散射的物理模型。对各向同性散射介质,在非相干性假设条件下,导出了偏振光双散射和多散射前向散射的有效Mueller矩阵,给出了偏振光Mie散射前向有效Mueller矩阵各矩阵元之间的对称性关系,即Mueller矩阵的16个矩阵元中只有7个是独立的,其他9个矩阵元通过组合及一定角度的旋转即可得到。利用Monte Carol方法模拟了偏振光在空间传输10km的前向散射的有效Mueller矩阵,模拟结果表明各矩阵元存在一定的对称性关系,与基于本模型导出的偏振光前向散射的有效Mueller矩阵元具有较好的一致性。     

Heisenberg对应原理下氢原子1/r矩阵元的量子-经典对应

通过详细计算表明,在准经典情况下,氢原子1r的矩阵元的量子力学结果与它的Heisenberg矩阵元近似相等,在经典极限下,它们相同. 关键词： 量子力学 对应原理     

Proximity-induced subgaps in andreev billiards

We examine the density of states of an Andreev billiard and show that any billiard with a finite upper cutoff in the path length distribution P(s) will possess an energy gap on the scale of the Thouless energy. An exact quantum mechanical calculation for different Andreev billiards gives good agreement with the semiclassical predictions when the energy dependent phase shift for Andreev reflections is properly taken into account. Based on this new semiclassical Bohr-Sommerfeld approximation of the density of states, we derive a simple formula for the energy gap. We show that the energy gap, in units of Thouless energy, may exceed the value predicted earlier from random matrix theory for chaotic billiards.     

Semiclassical theory of integrable and rough Andreev billiards

We study the effect on the density of states in mesoscopic ballistic billiards to which a superconducting lead is attached. The expression for the density of states is derived in the semiclassical S-matrix formalism shedding light onto the origin of the differences between the semiclassical theory and the corresponding result derived from random matrix models. Applications to a square billiard geometry and billiards with boundary roughness are discussed. The saturation of the quasiparticle excitation spectrum is related to the classical dynamics of the billiard. The influence of weak magnetic fields on the proximity effect in rough Andreev billiards is discussed and an analytical formula is derived. The semiclassical theory provides an interpretation for the suppression of the proximity effect in the presence of magnetic fields as a coherence effect of time reversed trajectories. It is shown to be in good agreement with quantum mechanical calculations. Received 21 August 1999 and Received in final form 21 March 2001     

Semiclassical limit for a truncated Hamiltonian

In the numerical calculation of the eigenenergies of a polynomial Hamiltonian, the majority of the levels depend on the cutoff of the basis used. By analyzing the finite Hamiltonian matrix as corresponding to a classical "Action Billiard" we are able to explain several features of the full spectrum using semiclassical periodic orbit theory. There are a large number of low-period orbits which interfere at the higher energies contained in the billiard. In this range the billiard becomes more regular than the untruncated Hamiltonian, as reflected by the Berry-Robnik level spacing distribution. (c) 1996 American Institute of Physics.     

Quantenfeldtheorie wechselwirkender Vielteilchensysteme zur semiklassischen Beschreibung von kollektiver Bewegung mit großen Amplituden

By using path integral methods a collective quantum field theory of interacting many-body systems is developed, the classical limit of which is given by the time-dependent mean-field approximation. In this way the mean-field approximation is embedded into the full quantum mechanics and the quantum corrections to the “classical” mean-field approximation can be systematically evaluated. By including the dominant quantum corrections to the mean-field approximation a semiclassical theory of large amplitude collective motions in many-body-systems, which show a highly nonlinear dynamic and are not accessible to perturbation theoretical methods, is derived. The semiclassical theory is developed explicitly for bound states and decay processes like nuclear fission. In the case of bound states this leads to the quantization of the time-dependent Hartree-Fock-Theory, which is demonstrated for a uniform nuclear rotation.     

Conductance fluctuations and quantum chaotic scattering in semiconductor microstructures

We review recent experiments on aperiodic conductance fluctuations in ballistic GaAs/AlGaAs microstructures in the shape of a stadium billiard and a circle with point-contact leads, measured at millikelvin temperatures. Much of the observed behavior can be analyzed within a semiclassical approach to quantum chaotic scattering. After a brief review of the Landauer-Buttiker formulation of coherent transport, a variety of novel experimental phenomena and comparisons to semiclassical theory are presented. In particular, we discuss quantum-enhanced backscattering, the power spectrum of conductance fluctuations, crossover to the high-magnetic-field and tunneling regimes, and an application allowing the rate of phase-randomizing scattering to be measured in chaotic ballistic microstructures.     

复杂势场量子弹球中疤痕态的量子化条件

量子疤痕是波函数在经典不稳定周期轨道周围反常凝聚的一种量子或波动现象.人们对疤痕态的量子化条件进行了大量研究,对深入理解半经典量子化起到了一定的促进作用.之前大部分研究工作主要集中在硬墙量子弹球上,即给定边界形状的无穷深量子势阱系统.本文研究具有光滑复杂势场的二维量子弹球系统,考察疤痕态的量子化条件及其重复出现的规律,得到了与硬墙弹球不一样的结果,对理解这类现象是一个有益的补充.这些结果将有助于理解具有无规长程杂质分布的二维电子系统的态密度谱和输运行为.     

Semiclassical matrix model for quantum chaotic transport with time-reversal symmetry

We show that the semiclassical approach to chaotic quantum transport in the presence of time-reversal symmetry can be described by a matrix model. In other words, we construct a matrix integral whose perturbative expansion satisfies the semiclassical diagrammatic rules for the calculation of transport statistics. One of the virtues of this approach is that it leads very naturally to the semiclassical derivation of universal predictions from random matrix theory.