Studies on integrable non-equilibrium statistical mechanical models
| Project/Area Number |
15K05203
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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 Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 非平衡 / 揺らぎ / 厳密解 / 非平衡統計力学 / KPZ普遍性 / ランダム行列 / 流体力学 / 非平衡揺らぎ / 揺らぐ流体力学 / 排他過程 / 頂点模型 / 大偏差 |
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| Outline of Final Research Achievements |
During the research period, we have achieved several novel results on the studies of non-equilibrium statistical mechanical models with integrable structures. First we invented a
new approach to study various models in the Kardar-Parisi-Zhang (KPZ) universality class. In particular we applied the techniques to the stochastic six vertex model, which is considered to be a fundamental model in the KPZ class. Second, we have generalized an analysis which has been developed for the single component systems to a multi-species model known as the AHR model. This is also considered as the first confirmation of a prediction of a conjectural theory called the nonlinear fluctuating hydrodynamics, which has been recently successfully applied to various systems with
nonlinear interaction. We have also studied the current fluctuations in a quantum spin chain and succeeded in finding an exact solution for its large deviation. The connection to random matrix theory was observed.
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| Academic Significance and Societal Importance of the Research Achievements |
まずKPZ系に対して開発した新手法は、従来の手法にあった発散の問題が回避されており多くのモデル系に対して統一的に適用することが可能であり、近年進展が著しい可積分確率と呼ばれる分野における重要な貢献である。また多成分系に対する手法の一般化と普遍揺らぎを決定したことは、可積分非平衡系の手法の適用範囲を大いに広げ今後の発展性が高いものであるとともに、揺らぐ流体力学と呼ばれる有効理論の予言をミクロな計算から検証する最初の例も与えるものであった。さらに、量子スピン系に対するカレント揺らぎの決定とランダム行列理論との関係の発見は、新奇性が高く今後様々な方向への拡張、応用が期待される。
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Report
(6 results)
Research Products
(61 results)
