2012 Fiscal Year Final Research Report
Exotic quantum holonomy in eigenvalues and eigenspaces
| Project/Area Number |
22540396
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
TANAKA Atushi 首都大学東京, 理工学研究科, 助教 (20323264)
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| Co-Investigator(Renkei-kenkyūsha) |
CHEON Taksu 高知工科大学, 工学部, 教授 (60227353)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 新奇な量子ホロノミー / 例外点 / 量子回路 / フロケ作用素 / 量子写像 |
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| Research Abstract |
The geometric phase is the most famous example of quantum holonomy, where an adiabatic cycle induces a nontrivial change for Examples of the quantum holonomy of exotic kind (also known as Cheon's anholonomies) have been found, where eigenenergies (or quasienergies) as well as eigenspaces of bound states exhibit multiple-valuedness in the parameter space. Through this research project, the theory of the exotic quantum holonomy has been further developed. Also, new examples of the exotic quantum holonomy have been found. Although the present results are purely theoretical, it is expected that the further study along this line will lead to the experimental realization of the exotic quantum holonomy.
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