| Project/Area Number |
21654053
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Single-year Grants |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyushu University (2011)
Naruto University of Education (2009-2010) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MURKAMI Hitoshi 東京工業大学, 理工学研究科, 准教授 (70192771)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥3,370,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2009: ¥1,200,000 (Direct Cost: ¥1,200,000)
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| Keywords | トポロジー / 結び目理論 / 量子情報 / 量子不変量 / エントロピー / 結び目 / 量子計算 / 共形場理論 / チャーン・サイモンズ不変量 |
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| Research Abstract |
Entanglement entropy is one of the characteristic quantities in the topological quantum computation. The entanglement entropy, especially topological entanglement entropy, is intimately related to the quantum invariants of knots and 3-manifolds. We studied the colored Jones polynomials for knots and links. We exactly analyzed the colored Jones polynomial for torus knots, and we obtained explicit relationship with classical topological invariants such as torsions. We also studied the Fourier expansion of modular forms, and obtained a relationship between their asymptotic behavior and the entropy of complex manifolds.
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