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Analysis of the spectral structure of Dirac operators

Research Project

Project/Area Number 21540187
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionEhime University

Principal Investigator

ITO Hiroshi  愛媛大学, 大学院・理工学研究科, 教授 (90243005)

Co-Investigator(Renkei-kenkyūsha) YAMADA Osanobu  立命館大学, 理工学部, 教授 (70066744)
TAMURA Hideo  岡山大学, 理学部, 教授 (30022734)
NOMURA Yuji  愛媛大学, 理工学研究科, 准教授 (40282818)
MINE Takuya  京都工芸繊維大学, 工芸科学研究科, 准教授 (90378597)
IWATSUKA Akira  京都工芸繊維大学, 工芸科学研究科, 教授 (40184890)
KADOWAKI Mitsuteru  愛媛大学, 理工学研究科, 准教授 (70300548)
Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Keywords関数解析 / 数理物理 / スペクトル理論 / ディラック作用素 / レゾナンス / 相対論的シュレディンガー作用素 / 固有値 / スペクトル / シュレーディンガー作用素 / 非相対論的極限
Research Abstract

We have investigated the spectral property and the nonrelativistic limit of the relativistic Hamiltonians with a dilation analytic potential diverging at infinity. In particular, we showed that resonances of the Dirac operator appear near resonances of some two Schrodinger operators if the speed of light is sufficiently large. The analysis is based on an abstract theorem proved in this work. The theorem is useful to determine the spectral property of a self-adjoint operator defined as a boundary value of some analytic family of closed operators.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (35 results)

All 2011 2010 2009 Other

All Journal Article (14 results) (of which Peer Reviewed: 14 results) Presentation (21 results)

  • [Journal Article] Relativistic Hamiltonians with dilation analytic potentials diverging at infinity2011

    • Author(s)
      Ito, Hiroshi T. and Yamada, Osanobu
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 68no.4 Pages: 1-47

    • NAID

      10030344887

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Aharonov-Bohm effect in resonances of magnetic Schrodinger operators with potentials with supports at large separation2011

    • Author(s)
      Alexandrova, Ivana and Tamura, Hideo
    • Journal Title

      Ann. Henri Poincare

      Volume: 12no.4 Pages: 679-721

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Resonance free regions in magnetic scattering by two solenoidal fields at large separation2011

    • Author(s)
      Alexandrova, Ivana and Tamura, Hideo
    • Journal Title

      Journal of Functional Analysis

      Volume: 260no.6 Pages: 1836-1885

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On scattering for wave equations with dissipative terms in layered media2011

    • Author(s)
      Kadowaki, Mitsuteru and Nakazawa, Hideo and Watanabe Kazuo
    • Journal Title

      Electron. J. Diff. Equ.

      Volume: 2011No.65 Pages: 1-18

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relativistic Hamiltonians with dilation analytic potentials diverging at infinity2011

    • Author(s)
      Hiroshi T.Ito
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 68 Pages: 1-47

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the nonrelativistic limit of Dirac operators with potentials diverging at infinity2010

    • Author(s)
      Ito, Hiroshi T. and Yamada, Osanobu
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B16 Pages: 75-89

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The spectrum of Schrodinger operators with periodic Aharonov-Bohm magnetic fields2010

    • Author(s)
      Mine, Takuya and Nomura Yuji
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B16 Pages: 135-140

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the nonrelativistic limit of Dirac operators with potentials diverging at infinity2010

    • Author(s)
      Hiroshi Ito
    • Journal Title

      Spectral and Scattering Theory and Related Topics, RIMS Kokyuroku Bessatsu

      Volume: B16 Pages: 75-89

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the nonrelativistic limit of Dirac operators with potentials diverging at infinity2010

    • Author(s)
      Hiroshi Ito
    • Journal Title

      Spectral and Scattering Theory and Related Topics" Kokyuroku Bessatsu, Vol.B16, 2010 B16(掲載確定)

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Norm resolvent convergence to Schrodinger operators with infinitesimally thin toroidal magnetic fields, Spectral and scattering theory for quantum magnetic systems2009

    • Author(s)
      Iwatsuka, Akira and Mine, Takuya and Shimada, Shin-ichi
    • Journal Title

      Contemp. Math.

      Volume: 500 Pages: 139-151

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] A spectral approach to the Dirac equation in the non-extreme Kerr-Newmann metric2009

    • Author(s)
      Winklmeier, Monika and Yamada, Osanobu
    • Journal Title

      J. Phys.

      Volume: 42no.29 Pages: 295204-15

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The spectrum of Schrodinger operators with random δ magnetic fields2009

    • Author(s)
      Takuya Mine
    • Journal Title

      Annales de l'Institut Fourier 59(2)

      Pages: 659-689

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Norm resolvent convergence to Schrodinger operators with infinitesimally thin toroidal magnetic fields2009

    • Author(s)
      Akira IWATSUKA
    • Journal Title

      Sectral and Scattering Theory for Quantum Magnetic System, Contemporary Mathematics 500

      Pages: 139-151

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Relativistic Hamiltonians with dilation analytic potentials diverging at infinity

    • Author(s)
      Hiroshi Ito
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: (掲載確定)

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Presentation] Explicit solutions for Schrodinger equations with Aharonov-Bohm magnetic fields2011

    • Author(s)
      峯拓矢
    • Organizer
      RIMS研究集会「スペクトル散乱理論とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-12-16
    • Related Report
      2011 Final Research Report
  • [Presentation] ディラック作用素のレゾナンスについて2011

    • Author(s)
      伊藤宏
    • Organizer
      第18回超局所解析と古典解析
    • Place of Presentation
      かんぽの宿伊野
    • Year and Date
      2011-11-26
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Dirac作用素の極限吸収原理について2011

    • Author(s)
      山田修宣
    • Organizer
      第18回超局所解析と古典解析
    • Place of Presentation
      かんぽの宿伊野
    • Year and Date
      2011-11-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Bethe-Sommerfeld予想について2011

    • Author(s)
      峯拓矢
    • Organizer
      第18回超局所解析と古典解析
    • Place of Presentation
      かんぽの宿伊野
    • Year and Date
      2011-11-26
    • Related Report
      2011 Final Research Report
  • [Presentation] 3次元半空間の波動伝播と定常位相の方法について2011

    • Author(s)
      門脇光輝
    • Organizer
      2011年夏の作用素論シンポジウム
    • Place of Presentation
      熊本市国際交流会館
    • Year and Date
      2011-09-04
    • Related Report
      2011 Final Research Report
  • [Presentation] ディラック作用素のスペクトルについて2011

    • Author(s)
      伊藤宏
    • Organizer
      2011年夏の作用素論シンポジウム
    • Place of Presentation
      熊本市国際交流会館
    • Year and Date
      2011-09-03
    • Related Report
      2011 Final Research Report
  • [Presentation] The limiting absorption method for Dirac operators in the non-extreme Kerr-Newman metric2011

    • Author(s)
      山田修宣
    • Organizer
      2011年夏の作用素論シンポジウム
    • Place of Presentation
      熊本市国際交流会館
    • Year and Date
      2011-09-03
    • Related Report
      2011 Final Research Report
  • [Presentation] 磁場散乱におけるレゾナンスとAB効果III2011

    • Author(s)
      田村英男
    • Organizer
      2011年夏の作用素論シンポジウム
    • Place of Presentation
      熊本市国際交流会館
    • Year and Date
      2011-09-03
    • Related Report
      2011 Final Research Report
  • [Presentation] 遠方で発散するポテンシャルをもつ相対論的ハミルトニアンについて2011

    • Author(s)
      伊藤宏
    • Organizer
      解析セミナー
    • Place of Presentation
      愛媛大学
    • Year and Date
      2011-06-17
    • Related Report
      2011 Final Research Report
  • [Presentation] 磁場散乱におけるレゾナンスとAB効果II2011

    • Author(s)
      田村英男
    • Organizer
      作用素論セミナー
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-04-22
    • Related Report
      2011 Final Research Report
  • [Presentation] Relativistic Hamiltonians with dilation analytic potentials diverging at infinity2011

    • Author(s)
      山田修宣
    • Organizer
      偏微分方程式姫路研究集会
    • Place of Presentation
      イーグレ姫路
    • Year and Date
      2011-02-19
    • Related Report
      2011 Final Research Report
  • [Presentation] The spectrum of the Aharonov-Bohm Hamiltonian on the hyperbolic plan2011

    • Author(s)
      峯拓矢
    • Organizer
      RIMS workshop" Spectral and scattering Theory and related topics
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2011-02-17
    • Related Report
      2011 Final Research Report
  • [Presentation] 上半平面上のAharonov-Bohm磁場2010

    • Author(s)
      野村祐司
    • Organizer
      第17回超局所解析と古典解析
    • Place of Presentation
      かんぽの宿山代
    • Year and Date
      2010-11-21
    • Related Report
      2011 Final Research Report
  • [Presentation] Dirac作用素の極限吸収原理について2010

    • Author(s)
      山田修宣
    • Organizer
      第17回超局所解析と古典解析
    • Place of Presentation
      かんぽの宿山代
    • Year and Date
      2010-11-20
    • Related Report
      2011 Final Research Report
  • [Presentation] 遠方で非有界なポテンシャルをもつハミルトニアンについて2010

    • Author(s)
      伊藤宏
    • Organizer
      第17回超局所解析と古典解析
    • Place of Presentation
      かんぽの宿山代
    • Year and Date
      2010-11-20
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] 磁場散乱におけるレゾナンスとAB効果2010

    • Author(s)
      田村英男
    • Organizer
      2011年夏の作用素論シンポジウム
    • Place of Presentation
      松本市中央公民館Mウィング南
    • Year and Date
      2010-09-04
    • Related Report
      2011 Final Research Report
  • [Presentation] 上半平面上のAharonov-Bohm磁場と保型形式の零点2010

    • Author(s)
      野村祐司
    • Organizer
      作用素論セミナー
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2010-06-25
    • Related Report
      2011 Final Research Report
  • [Presentation] 周期的およびランダムなAharonov-Bohm磁場をもつSchrodinger作用素のスペクトル2010

    • Author(s)
      野村祐司
    • Organizer
      日本数学会年会函数解析学分科会特別講演
    • Place of Presentation
      慶応大学矢上キャンパス
    • Year and Date
      2010-03-24
    • Related Report
      2011 Final Research Report
  • [Presentation] 周期的およびランダムな Aharonov-Bohm 磁場を持つ Schrodinger 作用素のスペクトル2010

    • Author(s)
      野村祐司
    • Organizer
      日本数学会2010年度年会
    • Place of Presentation
      慶應義塾大学理工学部
    • Year and Date
      2010-03-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] Spectral properties of Schrodinger operators with singular magnetic fields supported by circle in R^32009

    • Author(s)
      岩塚明, 島田伸一, 峯拓矢
    • Organizer
      RIMS研究集会「スペクトル・散乱理論とその周辺」
    • Place of Presentation
      京都大学
    • Year and Date
      2009-12-03
    • Related Report
      2011 Final Research Report
  • [Presentation] レゾンルベント評価と逆散乱問題2009

    • Author(s)
      伊藤宏
    • Organizer
      2009年夏の作用素論シンポジウム
    • Place of Presentation
      いわて県民情報交流センターアイーナ
    • Year and Date
      2009-09-07
    • Related Report
      2011 Final Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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