Topological Solitons and Low-Energy Phenomena on Noncommutative Space

非对易几何在量子霍尔(QH)系统中实现。QH系统中的带电激发是非对易的Skyrmions。另一方面，平行磁场以量子化的Sine-Gordon孤子通量的形式渗入双层系统。分析了Skyrmions粒子在Sine-Gordon孤子晶格上的散射过程，并与Sawada小组(京都大学)的实验结果进行了比较，两者符合得很好。其次，对不同馈电方式下双层量子氢系统中的类约瑟夫森现象进行了理论研究。我已经将结果与冯·克利津的团队(Max-Planck Institute)的实验结果进行了比较，结果吻合得很好。在非对易几何的框架下，我还分析了双层QH系统的斜反铁磁相中的Goldstone模。然后，我预言了自旋约瑟夫森流的存在。

Noncommutative geometry is realized in the quantum Hall (QH) system. Charged excitations in the QH system are noncommutative skyrmions. On the other hand, parallel magnetic field penetrates into the bilayer system as quantized sine-Gordon soliton fluxes. I have analyzed a scattering process of skyrmions against a sine-Gordon soliton lattice and compared the theoretical results with the experimental results due to Sawada's group (Kyoto University) with good agreement. Next, I made a theoretical study of the Josephson-like phenomena in a bilayer QH system for various way of feeding current to the system. I have compared the results with the experimental results due to von Klitzing's group (Max-Planck Institute) with good agreement. I have also analyzed Goldstone modes in the canted antiferromagnetic phase of the bilayer QH system within the framework of the noncommutative geometry. Then, I have predicted the existence of spin-Josephson current.