2011 Fiscal Year Final Research Report
Mathematical physics of exotic quantum holonomy
| Project/Area Number |
21540402
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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 | Kochi University of Technology |
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Principal Investigator |
ZEN Takusu 高知工科大学, 環境理工学群, 教授 (60227353)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 量子力学 / 量子制御 / 断熱過程 / 固有順位 / 時間周期系 |
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| Research Abstract |
The exotic quantum holonomy refers to the anholonomy of quantum states other than that of the quantum phases. It involves the exchange of eigenstates after the cyclic variation of system parameters. We have created a gauge theoretical formulation that describes both the exotic and conventional quantum holonomy, the Berry phase, in a unified fashion. It has enabled the discovery of exceptional points located at the complexified parameter value which act as branching points of the eigenenergies, and cause the exotic anholonomy along the real axis of the parameter space. It has also helped us systematically construct quantum systems with exotic anholonomy among multi-level eigenstates. In a system of a particle on Aharonov-Bohm ring, the exotic quantum holonomy has been shown to exist for non-adiabatic cyclic variation of the strength of the magnetic field.
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