2013 Fiscal Year Final Research Report
Research about supersymmetric higher dimensional non-commutative geometry and topologial quantum many-body states
| Project/Area Number |
23740212
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Particle/Nuclear/Cosmic ray/Astro physics
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| Research Institution | Kagawa National College of Technology |
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Principal Investigator |
HASEBE Kazuki 香川高等専門学校, 一般教育科, 講師 (60435469)
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| Project Period (FY) |
2011 – 2013
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| Keywords | 非可換幾何 / 量子スピン系 / トポロジカル絶縁体 / 非エルミート量子力学 / 超対称性 / 南部括弧 |
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| Research Abstract |
We established supersymmetric higher dimensional non-commutative geomery and applied its mathematics to the topological matters. In 2011, we explored non-commutative geometry for supersymmetric higher dimensional spheres and hyperboloids. Besides, we applied the mathematics to the supersymmetric quantum spin systems and non-Hermitian quantum mechanics and exploited their topological structures such as edge states and hidden order. In 2012, we further investigated the supersymmetric quantum spin systems especially about the recently proposed quantum entanglement. In 2013, we applied the non-commutative geometry to the topological insulators (in particular A-class nad AIII-class) and analyzed their physical properties.
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