Tetrahedron equation and quantum integrable systems
| Project/Area Number |
15K04892
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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 |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Kuniba Atsuo 東京大学, 大学院総合文化研究科, 教授 (70211886)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
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)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 可積分系 / マルコフ過程 / 量子群 / ヤン・バクスター方程式 / 四面体方程式 / 行列積 / 確率過程 / 非対称排他過程 / 非対称ゼロレンジ過程 / 組合せR / 結晶基底 |
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| Outline of Final Research Achievements |
An integrable model in Markov processes in non-equilibrium statistical mechanics was constructed. It is formulated as a stochastic dynamics of n kinds of particles on one-dimensional lattice obeying asymmetric transition rules. It includes a majority of such models which have been studied so far. The relation to the tetrahedron equation and the theory of crystal base of quantum groups was clarified and a matrix product formula was derived for the stationary states. They revealed the representation theoretical origin of the known algorithm to calculate stationary probabilities.
For n=2, density and current profile of the particles were derived and the physical aspects of the model was clarified both qualitatively and quantitatively.
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Report
(4 results)
Research Products
(35 results)
