Global level set structure of ultradiscrete integrable systems
| Project/Area Number |
22540241
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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 |
Global analysis
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| Research Institution | 防衛大学校 |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 可積分系 / セルオートマトン / 量子群 / トロピカル幾何学 / 超離散化 / 結晶基底 / 戸田格子 / 数理物理 / 統計力学 |
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| Research Abstract |
We found and proved a new mathematical formula in the field of combinatorics. That is called a fermionic formula for partition functions associated with level set of a periodic integrable cellular automaton. By inventing a cellular-automaton-like description in terms of two colored strips, we also succeeded to construct a family of commuting phase flows (generalized time evolutions) in tropical periodic Toda lattice, a special discrete limit of well known Toda lattice in the field of classical integrable systems. The phase flows are important to determine the structure of the phase space of this dynamical system.
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Report
(4 results)
Research Products
(25 results)
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[Presentation] 周期箱玉系の等位集合2011
Author(s)
高木太一郎
Organizer
数理物理・物性基礎論セミナー
Place of Presentation
お茶の水女子大学(東京都)(招待講演)
Year and Date
2011-06-18
Related Report
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