Studies on random fractals and integrable stochastic processes
| Project/Area Number |
16K05468
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 University of Science |
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Principal Investigator |
Sakai Kazumitsu 東京理科大学, 理学部第二部物理学科, 准教授 (10397028)
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| Co-Investigator(Kenkyū-buntansha) |
茂木 康平 東京海洋大学, 学術研究院, 准教授 (30583033)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | Schramm-Loewner発展 / 可解模型 / 量子可積分系 / 共形場理論 / ベーテ仮説 / 輸送特性 / 対称多項式 / Grothendieck多項式 / 楕円対称関数 / Grassmann束 / ベーテ仮設 / スピン輸送 / 確率過程 / K理論 / スピン輸送特性 / グロタンディーク多項式 / 臨界現象 / 場の理論 / 可積分系 |
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| Outline of Final Research Achievements |
Geometric properties in the 2D critical phenomena can be classified by the Schramm-Loewner evolution. We have studied a relationship between SLE's and (1+1) quantum integrable systems. In particular, we found that SLE's with spin degrees of freedom can be associated with some quantum integrable systems. We have also investigated random fractals appearing in the critical 4-state Potts model and found a characteristic logarithmic behavior of crossing probabilities.
The partition functions of type B and C ice models have been investigated by using the quantum inverse scattering method. We have shown that the wavefunctions are expressed using generalizations of the symplectic Schur functions.
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| Academic Significance and Societal Importance of the Research Achievements |
２次元臨界現象にはフラクタルと呼ばれる特有の幾何構造が現れることが知られている．Schramm-Loewner発展(SLE)によって，これらのフラクタルは数学的に分類することができることがわかってきた．スピン自由度を付随させたSLEが(1+1)次元の量子可積分系と結びついている点を見出したことは意義がある．
また，数学的に重要な対称多項式の研究をを物理学における可解格子模型とその波動関数の研究に帰着させて発展させた点にも意義がある．
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Report
(5 results)
Research Products
(43 results)
