Number theory and geometry behind quantum interaction models

• Project/Area Number: 24K16941
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12010:Basic analysis-related
• Research Institution: NTT Communication Science Laboratories
• Principal Investigator: REYESBUSTOS CID 日本電信電話株式会社NTTコミュニケーション科学基礎研究所, 基礎数学研究P, 研究主任 (10991565)
• Project Period (FY): 2024-04-01 – 2027-03-31
• Project Status: Granted (Fiscal Year 2024)
• Budget Amount: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000); Fiscal Year 2026: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2025: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000); Fiscal Year 2024: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 量子相互作用 / 量子ラビ模型 / スペクトルゼータ関数 / 非可換調和振動子 / 隠れた対称性

Outline of Research at the Start

In this research project we study the mathematical structure of quantum models of light-matter interaction, focusing on the geometric structures of the spectrum (symmetry and degeneracy) and zeta functions associated with the energy levels of the models.