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Research on the binding condition and the renormalization for a quantum system of Bose field coupled to a particle

Research Project

Project/Area Number 16K17612
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Basic analysis
Research InstitutionShinshu University

Principal Investigator

Sasaki Itaru  信州大学, 学術研究院理学系, 准教授 (50558161)

Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywords数理物理 / スペクトル解析 / Rabiモデル / Bogoliubov変換 / 時間作用素 / 自己共役作用素 / 基底状態 / ハミルトニアン / 対角化 / 場の量子論 / 量子ウォーク / Pauli-Fierzモデル / 準相対論的Pauli-Fierzモデル / 量子場 / 相対論的量子力学 / 埋蔵固有値 / 関数解析 / 場の理論 / 作用素論
Outline of Final Research Achievements

(1) We proved a theorem that identifies the essential spectrum of discrete Laplacian by adding graph perturbation to a periodic graph. (2) We consider a generalized Rabi model, and we proved that the dressed photon appears in the ground state in a deep-strong coupling regime. (3) It is constructed that Schrodinger operators with slowly decaying potential that has a positive energy embedded eigenvalue. (4) Time operators for quantum walks are considered, and various examples are constructed. It is clarified that the relationship between the winding numbers and self-adjoint expansions of a time operator. (5) Algebraic Bogoliubov transformations that diagonalize the Hamiltonian of a pair theory are developed.

Academic Significance and Societal Importance of the Research Achievements

上の成果の(1)は物性物理学に関連する結果であり,周期構造を持つグラフの本質的スペクトルが特定されることにより,本質的スペクトルの外にある固有値の数値計算が保証されるようになる。(2)は量子デバイスに関連する数学的結果である。(3)(4)(5)は量子物理系の数学的構造に関する研究である。

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (18 results)

All 2019 2018 2017 2016 Other

All Journal Article (3 results) (of which Int'l Joint Research: 3 results,  Peer Reviewed: 3 results,  Acknowledgement Compliant: 1 results) Presentation (11 results) (of which Int'l Joint Research: 5 results,  Invited: 7 results) Remarks (4 results)

  • [Journal Article] A mathematical analysis of dressed photon in ground state of generalized quantum Rabi model using pair theory2017

    • Author(s)
      Hirokawa Masao, Moeller Jacob S, Sasaki Itaru
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical

      Volume: 50 Issue: 18 Pages: 184003-184003

    • DOI

      10.1088/1751-8121/aa677c

    • Related Report
      2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Embedded eigenvalues and Neumann-Wigner potentials for relativistic Schroedinger operators2017

    • Author(s)
      Itaru Sasaki, Jozsef Lorinczi
    • Journal Title

      Journal of Functional Analysis

      Volume: In press Issue: 4 Pages: 1548-1575

    • DOI

      10.1016/j.jfa.2017.03.012

    • Related Report
      2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Essential spectrum of the discrete Laplacian on a perturbed periodic graph2017

    • Author(s)
      Itaru Sasaki, Akito Suzuki
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 446 Issue: 2 Pages: 1863-1881

    • DOI

      10.1016/j.jmaa.2016.09.063

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Regular Bogoliubov Transformations2019

    • Author(s)
      佐々木格
    • Organizer
      RIMS研究集会「量子場の数理とその周辺」
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 準相対論的 Pauli-Fierz モデルにおける粒子の束縛について2019

    • Author(s)
      佐々木格
    • Organizer
      新井朝雄先生退職記念研究集会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Existence of ground state of the model of a massless charged particle interacting with the quantized radiation field2018

    • Author(s)
      佐々木格
    • Organizer
      量子場の数理とその周辺
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Existence of ground state of massless relativistic Pauli-Fierz model2018

    • Author(s)
      Itaru Sasaki
    • Organizer
      ICMP(国際数理物理学会)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] Existence of ground state in the massless semi-relativistic Pauli-Fierz model2018

    • Author(s)
      佐々木格
    • Organizer
      The 16th Linear and Nonlinear Waves
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] On the spectral analysis of the semi-relativistic Pauli-Fierz model2018

    • Author(s)
      佐々木格
    • Organizer
      スペクトル・散乱理論とその周辺
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 準相対論的 Pauli-Fierz モデルの基底状態について---粒子が質量を 持たない場合---2018

    • Author(s)
      佐々木格
    • Organizer
      Workshop on Analysis in Kagurazaka 2018
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Embedded Eigenvalues and Neumann-Wigner Potentials for Relativistic Schrodinger Operators2017

    • Author(s)
      Itaru Sasaki
    • Organizer
      Physical and mathematical approaches to interacting particle systems ―In honer of 70th birthday of Herbert Spohn
    • Place of Presentation
      Tokyo Institute of Technology
    • Year and Date
      2017-01-12
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On the embedded eigenvalue of relativistic Schrodinger operator2017

    • Author(s)
      Itaru Sasaki
    • Organizer
      Aarhus University, Math/Phys Seminar
    • Related Report
      2017 Research-status Report
  • [Presentation] Embedded Eigenvalue and von Neumann-Wigner Potential for the Relativistic Schrodinger Operator2017

    • Author(s)
      Itaru Sasaki
    • Organizer
      University of Lorraine, Spectral Theory and Mathematical Physics
    • Related Report
      2017 Research-status Report
  • [Presentation] Embedded Eigenvalues and Neumann-Wigner Potentials for Relativistic Schrodinger Operators2016

    • Author(s)
      Itaru Sasaki
    • Organizer
      QMath13: Mathematical Results in Quantum Physics
    • Place of Presentation
      Georgia Institute of Technology(アメリカ)
    • Year and Date
      2016-10-09
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Remarks] 佐々木格のホームページ

    • URL

      http://math.shinshu-u.ac.jp/~isasaki/index.html

    • Related Report
      2018 Research-status Report
  • [Remarks] 信州大学研究者総覧SOAR: 佐々木格

    • URL

      http://soar-rd.shinshu-u.ac.jp/profile/ja.HFAVjFkV.html

    • Related Report
      2017 Research-status Report
  • [Remarks] 研究業績(佐々木格)

    • URL

      http://math.shinshu-u.ac.jp/~isasaki/gyoseki.html

    • Related Report
      2017 Research-status Report
  • [Remarks] 信州大学研究者総覧

    • URL

      http://soar-rd.shinshu-u.ac.jp/profile/ja.HFAVjFkV.html

    • Related Report
      2016 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2021-02-19  

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