• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Quantum Interaction and number, representation theory, discrete dynamics

Research Project

Project/Area Number 20K03560
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 11010:Algebra-related
Research InstitutionNTT Communication Science Laboratories (2021-2022)
Tokyo University of Science (2020)

Principal Investigator

Wakayama Masato  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, メディア情報研究部, 数学研究プリンシパル (40201149)

Project Period (FY) 2020-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2022: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2020: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords非可換調和振動子 / 量子ラビモデル / 保型形式 / 熱核 / 無限対称群 / スペクトルゼータ関数 / 特殊値 / 楕円曲線 / 超楕円曲線 / Eichler形式 / 数論 / 量子ラビ模型 / 表現論 / アペリ数 / スペクトルゼータ / 量子光学 / 非対称量子ラビ模型 / アペリ数類似
Outline of Research at the Start

非可換調和振動子と量子ラビモデルのスペクトルゼータ関数の特殊値の解析から現れる数論的対象(アペリ類似性の合同性、概保型形式、関連するコホモロジー)の研究を行う。これらにより進む量子相互作用に関する数論的・表現論的理解と、離散力学系・グラフ理論からのアイデアを駆使し、どうして、このような量子相互作用の背景に豊かな数論が展開されていくのかを追求する。また、それらの熱核から得られる分配関数の研究を通じて、量子相互モデルと数論との興味ある関係を発見していく。

Outline of Final Research Achievements

Non-commutative harmonic oscillators (NCHO), quantum Rabi models (QRM), and asymmetric quantum Rabi models (AQRM) are treated as quantum interactions in this project. Focusing on each Hein ODE picture, NCHO can be regarded as covering his QRM due to the confluence of singularities. The results are as follows: (1) Arithmetic research on special values of NCHO's spectral zeta function (automorphic forms, family of elliptic curves, generalizations of Eichler forms and their cohomology, congruences of Apelli-like numbers). (2) Description of degeneracy of AQRM, research on hidden symmetry, and proposal of conjectures linking the two. (3) Derivation of the heat kernel and partition functions of QRM by representation theory of infinite symmetric groups, function analysis, the oscillator representation of the SL_2 on the finite field F_2, and graph theory.

Academic Significance and Societal Importance of the Research Achievements

量子光学や固体物理において光と物質の最も基本的な相互作用を記述するモデルであり、超伝導を用いた qubit を作る実験結果を予測していた量子ラビ模型及び非対称ラビ模型は、量子情報科学において量子計算機作りにも深く関係しているが、その背後にある数論や表現論・幾何学的構造を(一部分ではあるが)具体的に見出す研究を行った。これは、物理と数学を結びつける一つの意義深い成果であるとともに、ここでの数学解析が、量子情報科学の発展に幾許かの寄与がなされる点で、学術的意義は大きい。

Report

(4 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • Research Products

    (20 results)

All 2023 2022 2021 2020 2019 Other

All Int'l Joint Research (1 results) Journal Article (9 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 8 results,  Open Access: 1 results) Presentation (8 results) (of which Int'l Joint Research: 2 results,  Invited: 8 results) Remarks (2 results)

  • [Int'l Joint Research] University of Augsburg(ドイツ)

    • Related Report
      2021 Research-status Report
  • [Journal Article] Heat kernel for the quantum Rabi model2022

    • Author(s)
      Reyes-Bustos Cid、Wakayama Masato
    • Journal Title

      Advances in Theoretical and Mathematical Physics

      Volume: 26 Issue: 5 Pages: 1347-1447

    • DOI

      10.4310/atmp.2022.v26.n5.a8

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Degeneracy and hidden symmetry -an asymmetric quantum Rabi model with an integer bias2022

    • Author(s)
      C. Reyes-Bustos and M. Wakayama
    • Journal Title

      Communications in Number Theory and Physics

      Volume: 16 Issue: 3 Pages: 615-672

    • DOI

      10.4310/cntp.2022.v16.n3.a4

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Apery-like numbers for non-commutative harmonic oscillators and automorphic integrals2022

    • Author(s)
      Kazufumi Kimoto, Masato Wakayama
    • Journal Title

      Annals de l’Institut Henri Poincare; - D, (Accepted 2020)

      Volume: 2020受理

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Heat kernel for the quantum Rabi model: II. Propagators and spectral determinants2021

    • Author(s)
      Cid Reyes-Bustos and Masato Wakayama
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 54-11 Issue: 11 Pages: 115202-115233

    • DOI

      10.1088/1751-8121/abdca7

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Remarks on the hidden symmetry of the asymmetric quantum Rabi model2021

    • Author(s)
      Cid Reyes-Bustos, Daniel Braak and Masato Wakayama
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 54-28 Issue: 28 Pages: 285202-285216

    • DOI

      10.1088/1751-8121/ac0508

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] 光とゼータ関数の特殊値 (Photons and special values of zeta functions)2021

    • Author(s)
      若山正人
    • Journal Title

      日本数学会 数学通信

      Volume: No.25 Pages: 24-25

    • Related Report
      2020 Research-status Report
  • [Journal Article] Heat kernel for the quantum Rabi model: II. Propagators and spectral determinants2021

    • Author(s)
      Cid Reyes-Bustos,Masato Wakayama
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: - Pages: 1-51

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Apery-like numbers for non-commutative harmonic oscillators and automorphic integrals2020

    • Author(s)
      K. Kimoto and M. Wakayama
    • Journal Title

      Annals de l’Institut Henri Poincare - D

      Volume: - Issue: 2 Pages: 1-53

    • DOI

      10.4171/aihpd/129

    • Related Report
      2022 Annual Research Report 2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Determinant expressions of constraint polynomials and the spectrum of the asymmetric quantum Rabi model2019

    • Author(s)
      K. Kimoto, C. Reyes-Bustos and M. Wakayama
    • Journal Title

      International Mathematics Research Notices (in PRINTING, 87 pages)

      Volume: - Issue: 12 Pages: 9458-9544

    • DOI

      10.1093/imrn/rnaa034

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Presentation] Geometric and algebraic problems on quantum interaction models2023

    • Author(s)
      Masato Wakayama
    • Organizer
      Geometry Seminar, Department of Mathematics, Radboud University Nijmegen
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Heat Kernels of Quantum Interaction Models for Quantum Computers2023

    • Author(s)
      Masato Wakayama
    • Organizer
      SIAM Computational Science and Engineering 2023, Part of MS302 Mathematics for Industry in the Asia Pacific Area
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Algebra and geometry for quantum interaction models2023

    • Author(s)
      Masato Wakayama
    • Organizer
      Colloquium, Department of Mathematics, University of Tubingen
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Geometric and algebraic problems on quantum interaction models2023

    • Author(s)
      Masato Wakayama
    • Organizer
      RIMS Kyoto University (Workshop on “Fields theory and related Topics”)
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Covering of asymmetric quantum Rabi models and possible zeta problems2023

    • Author(s)
      Masato Wakayama
    • Organizer
      Symposium “Rabi and Spin Boson models” Kyushu University, Fukuoka
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Quantum Interaction and Number Theory, Representation Theory - modular forms a bit beyond, infinite symmetric group, Fuchsian ODE2022

    • Author(s)
      Masato Wakayama
    • Organizer
      French-Japan Web-Seminar on Painleve; equations and related topics
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Quantum Interaction Models and Number Theory, Representation Theory2022

    • Author(s)
      Masato Wakayama
    • Organizer
      Colloquium, Department of Mathematics, University of Bologna
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] Interaction Models in Quantum Optics, Representation Theory and Number Theory2020

    • Author(s)
      Masato Wakayama
    • Organizer
      理化学研究所  iTHEMS コロキウム
    • Related Report
      2020 Research-status Report
    • Invited
  • [Remarks] 若山正人ウェブサイト(東京理科大学)

    • URL

      https://www.tus.ac.jp/ridai/doc/ji/RIJIA01Detail.php?act=nam&kin=ken&diu=72bb

    • Related Report
      2020 Research-status Report
  • [Remarks] 若山正人ウェブサイト(九州大学)

    • URL

      https://imi.kyushu-u.ac.jp/~wakayama/eindex.html

    • Related Report
      2020 Research-status Report

URL: 

Published: 2020-04-28   Modified: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi