Physical problems for which the existence of non-trivial topological Pauli phase (i.e. fractional quantization of angular orbital angular momenta that is possible in 2D case) is essential are discussed within the framework of two-dimensional Helmholtz, Schroedinger and Dirac equations.
As examples in classical field theory we consider a "wedge problem" -- a description of a field generated by a point charge between two conducting half-planes -- and a Fresnel diffraction from knife-edge.
In few-electron circular quantum dots the choice between integer and half-integer quantization of orbital angular momenta is defined by the Pauli principle. This is in line with precise experimental data for the ground state energy of such quantum dots in a perpendicular magnetic field.
In a gapless graphene, as in the case of gapped one, in the presence of overcharged impurity this problem can be solved experimentally, e.g., using the method of scanning tunnel spectroscopy.
Fractional quantization of ballistic conductance in 1D hole systems
本文分析了Si、Ge和GaAs系统中轻、重空穴带的弹道电导的分数量子化。结果表明，在连接两个准一维空穴引线的量子点接触区域中局域空穴态的形成大大改变了电导模式。局域空穴与传播空穴之间的交换作用导致了不同于电子系统的弹道电导分数量子化。附加平台处的电导值取决于轻空穴和重空穴能带之间的偏移Δ和交换相互作用常数的符号。对于Δ=0和铁磁交换作用，我们观察到在7 e ^{2}/4 h、3e^{2}/h和15 e ^{2}/4 h附近的额外平台，而反铁磁作用平台在e^{2}/4 h、e^{2}/h和9 e ^{2}/4 h附近形成。当Δ较大时，在e^2/h处形成单一平台。
Fractional quantization of Hall resistance as a consequence of mesoscopic feedback
介绍了一种非线性单粒子模型，它描述了系统在量子霍尔区的特性。该模型需要磁薛定谔方程与空间可变的磁通量密度。通量的分布是通过介观力学（MeM）的假设在我以前的文章中介绍[cf. J. Phys. Chem. Solids，65（2004），1507-1515; J. Geom. Phys.，第55/1（2005）卷，第1-18页]。该模型被发现意味着精确的整数和分数量子化的霍尔电导。事实上，在填充因子值$N/M$下，霍尔电阻为$R_H = \frac{h}{2e^2}\frac{M}{N}$。假设霍尔板的几何形状为矩形。具有介观反馈回路的磁薛定谔方程的特殊性质使我们能够证明霍尔电阻的量子化是电荷和通量量子化的直接结果。我相信这里给出的结果揭示了MeM在量子物理学中的整体地位，证实了它的有效性。
Quantum point contact with large localized spin: fractional quantization of the ballistic conductance
我们分析了包含大的局域自旋J的量子点接触的电导。如果只有一个传播通道呈现导电，则在弹道电导阶梯上形成额外的平台。该平台处的电导值强烈依赖于J，当J从1/2增加到无穷大时，电导值从3e^2/2 h减小到e^2/h，这与实验观察结果非常一致[D. J. Reilly等人，Phys.Rev.B63，121311（2001）]。
Fractional quantization of the ballistic conductance in electron and hole systems
本文对弹道电导0.7反常的理论作了简要的综述。特别注意的概念，分数量子化的弹道电导所产生的海森堡型交换相互作用之间的载流子之间的量子点接触区域和自由传播的载流子在电子和空穴系统。- Brotaskömmtun skotleienininnar í einvídum rafeinda og holukerfum granulesessari verdogur skömmtun skotleienininnar í einvídum kerfum útsketrandelogfir farienyfir noustu og helstu fræcilíkön á svietrii \LDQ 0，7 fráviksins \RDQ og tengdra fyribruga í einvídum rafeinda og holukerfum.海森伯的巨大潜力使他的一项艰巨的任务变得更加轻松，他跳过了数百万的太空堡垒，建造了一个更轻松的太空堡垒，建造了一个更轻松的框架，使海森伯的太空堡垒成为数百万的太空堡垒和一个巨大的堡垒。
Fractional quantization by interaction of arbitrary strength in gapless flat bands with divergent quantum geometry
HK Institute of Quantum Science & Technology, The University of Hong Kong（香港量子科学及技术研究院，香港大学）；State Key Laboratory of Optical Quantum Materials, The University of Hong Kong（光学量子材料国家重点实验室，香港大学）
