Construction and Application of Statisitical Mechanics for Random Curves and Patterns
| Project/Area Number |
21540397
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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 |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Chuo University |
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Principal Investigator |
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 非平衡統計力学 / 確率過程 / 数理物理学 / ランダム行列 / ランダムパターン / 統計力学 / 物性基礎論 / 数理物理 / 確率論 / 時空パターン / 共形不変性 / ブラウン運動 / 行列式過程 / マルコフ性 / 非対称単純排除過程 / 量子戸田格子 / パフ形式過程 / 相関関数 / 非衝突拡散過程 / 時空相関関数 / 複素ブラウン運動 / ループ除去経路 / 整関数 / Dyson模型 / 非衝突ブラウン運動 / 行列式点過程 / 量子ウォーク模型 / 相対論的量子力学 |
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| Research Abstract |
(1) We defined determinantal processes on spatio-temporal planes as generalizations of determinantal point processes.Using systems of multiple-orthogonal functions, we proved that the noncolliding Brownian motion and the noncolliding Bessel processes are determinantal processes for arbitrary initial configurations with finite numbers of particles, in which all spatio-temporal correlation functions of these processes are determined. We constructed nonequilibrium systems with an infinite number of particles and studied relaxation phenomena to equilibrium states.
(2) We introduced a new notion, a complex Brownian motion representation, for the noncolliding Brownian motion. If the system has this representation, we can prove that it is determinantal and all spatio-temporal correlation functions are obtained.
(3) We studied O'Connell process, which is related with the quantum Toda lattice. We formulated this proces as a generalization of the noncolliding Brownian motion.
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Report
(6 results)
Research Products
(85 results)
