| 研究課題/領域番号 |
21K20340
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| 研究種目 |
研究活動スタート支援
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| 配分区分 | 基金 |
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| 審査区分 |
0201:代数学、幾何学、解析学、応用数学およびその関連分野
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| 研究機関 | 沖縄科学技術大学院大学 |
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研究代表者 |
DELPORTE Nicolas 沖縄科学技術大学院大学, 重力、量子幾何と場の理論ユニット, ポストドクトラルスカラー (30913199)
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| 研究期間 (年度) |
2021-08-30 – 2025-03-31
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| 研究課題ステータス |
交付 (2023年度)
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| 配分額 *注記 |
2,860千円 (直接経費: 2,200千円、間接経費: 660千円)
2022年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
2021年度: 1,430千円 (直接経費: 1,100千円、間接経費: 330千円)
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| キーワード | dirac walk / trees / outlier / random tensors / Random walk / Self overlapping curve / Dirac operator / Random Graph / long-range / fermions / Random geometry / Quantum field theory / Renormalization |
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| 研究開始時の研究の概要 |
Within the context of quantum gravity, we would like to investigate the interaction between a random geometry and a quantum field, first through renormalization analysis and computation of the associated fixed points and conformal data. The originality of our proposal combines techniques from probability theory with those of quantum field theory to work on random geometries.
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| 研究実績の概要 |
1. In arXiv:2312.10881 (accepted in JPhysA), we have concluded our work on Dirac walks, that generalize the random walks adapted to scalar fields to Grassmann variables, where the walk goes from vertex to edge and edge to vertex, on regular trees. Through recursive equations that are exactly solvable in the case of trees, we obtain explicit expressions for two-point functions between any two sites (vertex or edge) of the graph and compute the associated spectral dimension, identical to that of scalar random walks.
2. In arxiv:2405.07731, we have studied the eigenvalue spectrum of order 3 random tensors with deviation and found a phase transition as the variance of the noise increases that leads to the emergence and merging of an outlier of the spectrum.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
The PhD student under our supervision has started to get more comfortable with the literature and tools, and we have a good collaboration ongoing with a professor of the YITP (Kyoto U).
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| 今後の研究の推進方策 |
1. We are setting up a study of the renormalization group flow of scalar fields on random locally tree-like graphs, using the formalism of FRG, using the spectral representation of the heat-kernel on the graph. We hope that this could later be generalized to more general graphs with loops.
2. We are looking at the spectrum of random tensors with more constrains such that can serve as the adjacency matrix of hypergraphs and hopefully return to the first point. The problem of the large order, as well as the distribution of complex eigenvalues, relevant in quantum information.
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