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Spectral Analysis on the Schroedinger Operators with Matrix Coefficients and Its Applications

Research Project

Project/Area Number 23540204
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionOkayama University

Principal Investigator

HIROKAWA Masao  岡山大学, 自然科学研究科, 教授 (70282788)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2011: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Keywords行列係数を持つシュレディンガー作用素 / ラビ模型 / 超対称性 / 自発的超対称性の破れ / ディラック作用素 / 自己共役拡張 / 境界条件 / 量子ビット / シュレディンガー作用素 / エネルギー準位交差 / 2準位原子 / 1モード・レーザー光 / 超対称量子力学 / カイラル性 / ラビ・ハミルトニアン / ジェインズ・カミングス・ハミルトニアン / 回路量子電磁力学 / 結合定数 / 強結合領域 / 超強結合領域 / 量子相転移
Research Abstract

I had studied the Schroedinger operators with matrix coefficients in the light of the problems for controlling and transporting qubit. As for the former problem, I had made spectral analysis for the Rabi model and the Janes-Cummings model describing a 2-level (artificial) atom coupled with a 1-mode photon. I had investigated the mathematical properties on the energy as the coupling strength between the atom and the photon get larger. As for the latter problem, I had performed the research into the characterization of the quantum tunneling phase factor and the clarification of its mathematical properties.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (12 results)

All 2014 2013 2012 2011 Other

All Journal Article (3 results) (of which Peer Reviewed: 2 results) Presentation (9 results) (of which Invited: 3 results)

  • [Journal Article] A Mathematical Aspect of A Tunnel-Junction for Spintronic Qubit2014

    • Author(s)
      M. Hirokawa and T. Kosaka
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 417 Issue: 2 Pages: 856-872

    • DOI

      10.1016/j.jmaa.2014.03.061

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] One-Dimensional Tunnel-Junction Formula for the Schrödinger Particle2013

    • Author(s)
      M. Hirokawa, T. Kosaka
    • Journal Title

      SIAM Journal on Applied Mathematics

      Volume: Vol.7 73 3, No.6 Issue: 6 Pages: 2247-2261

    • DOI

      10.1137/130929072

    • Related Report
      2013 Final Research Report
  • [Journal Article] One-Dimensional Tunnel-Junction Formula for Schringer Particle2013

    • Author(s)
      M. Hirokawa and T. Kosaka
    • Journal Title

      SIAM Journal on Applied Mathematics

      Volume: 73 Pages: 2247-2261

    • DOI

      10.1088/1742-6596/302/1/012044

    • Related Report
      2013 Annual Research Report 2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Tunnel-Junction Formulae with Application to Spintronic Qubit2013

    • Author(s)
      M. Hirokawa
    • Organizer
      Semiconductor Seminar
    • Place of Presentation
      Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
    • Year and Date
      2013-09-02
    • Related Report
      2013 Annual Research Report 2013 Final Research Report
  • [Presentation] (人工) 原子と光の相互作用の数理から量子デバイスへ2013

    • Author(s)
      廣川真男
    • Organizer
      計算材料科学と数学の協働によるスマート材料デザイン手法の探索--階層構造を解析する--
    • Place of Presentation
      東北大学WPI-AIMR 本館
    • Year and Date
      2013-03-15
    • Related Report
      2013 Final Research Report
  • [Presentation] On the coupling-strength increase of the Rabi model in the light of SUSYQM---from supersymmetric ground state to spontaneous supersymmetry breaking---2012

    • Author(s)
      M. Hirokawa
    • Organizer
      Spectral analysis of non-commutative harmonic oscillators and quantum devices
    • Place of Presentation
      九州大学大学院数理学研究院・IMI 棟
    • Year and Date
      2012-11-27
    • Related Report
      2013 Final Research Report
  • [Presentation] Transition between the regimes of strong and ultra-strong couplings in circuit QED2012

    • Author(s)
      M. Hirokawa
    • Organizer
      Workshop on "Avoided ? Crossing of Eigenvalue Curves" ---Non-commutative Harmonic Oscillator, Special Functions and Number Theory---
    • Place of Presentation
      九州大学稲盛財団記念館
    • Year and Date
      2012-03-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Some mathematical problems on Modeling in circuit quantum electrodynamics2011

    • Author(s)
      M. Hirokawa
    • Organizer
      Berliner Oberseminar Nichtlineare Partielle Differentialgleichungen
    • Place of Presentation
      Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
    • Year and Date
      2011-09-07
    • Related Report
      2013 Final Research Report
  • [Presentation] Some mathematical problems on modeling in circuit quantum electrodynamics,2011

    • Author(s)
      Masao Hirokawa
    • Organizer
      Berliner Oberseminar Nichtlineare Partielle Differentialgleichungen(招待講演)
    • Place of Presentation
      Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
    • Related Report
      2011 Research-status Report
  • [Presentation] On the coupling-strength increase of the Rabi model in the light of SUSYQM---from supersymmetric ground state to spontaneous supersymmetry breaking---

    • Author(s)
      Masao HIROKAWA
    • Organizer
      Workshop on "Spectral analysis of non-commutative harmonic oscillators and quantum devices"
    • Place of Presentation
      九州大学大学院数理学研究院
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] (人工) 原子と光の相互作用の数理から量子デバイスへ

    • Author(s)
      廣川真男
    • Organizer
      計算材料科学と数学の協働によるスマート材料デザイン手法の探索---階層構造を解析する---
    • Place of Presentation
      東北大学WPI-AIMR
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Tunnel-Junction Formula with Application to Electron

    • Author(s)
      Masao HIROKAWA
    • Organizer
      The 5th Math Mate Seminar
    • Place of Presentation
      東北大学WPI-AIMR
    • Related Report
      2012 Research-status Report
    • Invited

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Published: 2011-08-05   Modified: 2019-07-29  

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