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A study on the spectrum of Dirac operators

Research Project

Project/Area Number 18540196
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

YAMADA Osanobu  Ritsumeikan University, 理工学部, 教授 (70066744)

Co-Investigator(Kenkyū-buntansha) WATANABE Takuya  立命館大学, 理工学部, 助教 (80458009)
荒井 正治  立命館大学, 理工学部, 教授 (20066715)
大坂 博幸  立命館大学, 理工学部, 教授 (00244286)
伊藤 宏  愛媛大学, 理工学研究科, 教授 (90243005)
大鍛治 隆司  京都大学, 理学研究科, 准教授 (20160426)
Co-Investigator(Renkei-kenkyūsha) ARAI Masaharu  立命館大学, 理工学部, 教授 (20066715)
ITO Hiroshi  愛媛大学, 理工学研究科, 教授 (90243005)
OKAJI Takashi  京都大学, 理学研究科, 准教授 (20160426)
OSAKA Hiroyuki  立命館大学, 理工学部, 教授 (00244286)
Project Period (FY) 2006 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥3,920,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2007: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000)
Keywordsディラック方程式 / スペクトル理論 / 固有値問題 / 相対論的量子力学 / ディラック作用素 / スペクトル / Kerr-Newman距離 / 非相対論的極限 / ブラック・ホール / 相対性理論 / レゾナンス / スペクトル集中 / ブラックホール / 局所エネルギー / 固有関数 / 局所エネルギー減衰 / Kerr-Newnan距離
Research Abstract

We investigated spectral theory of Dirac operators.
Dirac operators appears in the relativistic quantum mechanics, while Schroedinger operators are studied in non-relativistic quantum mechanics. In the spectral theory of partial differential operators there are some differences between Dirac operators and Schroedinger operators、which are interesting points of our research. In the present research we have studied especially
(1) a connection between the spectrum of Dirac operators and the one of Schroedinger operators as the light speed c tends to infinity (article (3))
(2) the spectrum of Dirac operators in the Kerr-Newman metric, which appears in the black hole theory(articles (1), (12)).

Report

(6 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report   Self-evaluation Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (55 results)

All 2010 2009 2008 2007 2006 Other

All Journal Article (35 results) (of which Peer Reviewed: 24 results) Presentation (14 results) Book (5 results) Remarks (1 results)

  • [Journal Article] On the nonrelativistic limit of Dirac operators with potentials diverging at infinity2010

    • Author(s)
      H. Ito, O. Yamada
    • Journal Title

      RIMS Kokyuroku Bessatsu B16

      Pages: 75-89

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A singular Cauchy problem for the Euler-Poisson-Darboux equation2010

    • Author(s)
      J. Urabe, T. Watanabe
    • Journal Title

      J. Math. Pure Appl. 93

      Pages: 223-239

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the nonrelativistic limit of Dirac operators with potentials diverging at infinity2010

    • Author(s)
      H.T.Ito, O.Yamada
    • Journal Title

      RIMS Kokyuroku, Bessatsu B16

      Pages: 75-89

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A singular Cauchy problem for the Euler-Poisson-Darboux equation2010

    • Author(s)
      J.Urabe, T.Watanabe
    • Journal Title

      Journal de mathe'matiques pures et applique's 93

      Pages: 223-239

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A spectral approach to the Dirac equation in the Kerr-Newmann metric2009

    • Author(s)
      M. Winklmeier, O. Yamada
    • Journal Title

      Journal of Physics A: Mathematical and Theoretical 12

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Cancellation for inclusions of $C^*$-algebras of finite depth2009

    • Author(s)
      J.A. Jeong, H. Osaka, N.C. Phillips, T. Teruya
    • Journal Title

      Indiana Univ. Math. J. 58

      Pages: 1537-1564

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Rohlin property for inclusions of $C^*$-algebras with a finite Watatani index2009

    • Author(s)
      H. Osaka, K. Kodaka, T. Teruya
    • Journal Title

      Contemporary Math. 503

      Pages: 177-195

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Double pilling structure of matrix monotone functions and of matrix convex functions2009

    • Author(s)
      H. Osaka, J. Tomiyama
    • Journal Title

      Linear Algebra and its Applications 431

      Pages: 1825-1832

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] The best constant of Sobolev inequality which corresponds to Schroedinger operator with Dirac delta potential2009

    • Author(s)
      Y. Kametaka, H. Yamagishi, H. Watanabe, A. Nagai, K. Takemura, M. Arai
    • Journal Title

      Sci. Math. Jpn 69

      Pages: 211-225

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] A spectral approach to the Dirac equation in the Kerr-Newman metric2009

    • Author(s)
      M.Winklmeier, O.Yamada
    • Journal Title

      Journal of Physics A : Mathematical and Theoretical 42

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Adiabatic transition probability for small eigenvalue gap at two points2008

    • Author(s)
      T. Watanabe
    • Journal Title

      RIMS Kokyuroku Bessatsu B5

      Pages: 75-88

    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A spectral approach to the Dirac equation in the non-extreme Kerr-Newman metric2008

    • Author(s)
      M. Winklmeier and O. Yamada
    • Journal Title

      LANL Arxiv, Math-phys 0802.0402

      Pages: 1-15

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Adiabatic transition probability for small eigenvalue gap at two points2008

    • Author(s)
      Takuya Watanabe
    • Journal Title

      RIMS Kokyuroku Bessatsu (京都大学数理解析研究所講究録別冊) B5

      Pages: 75-88

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the local energy decay of solutions of the Dirac equation in non-extreme Kerr-Newman metric, I2008

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

      LANL ArXiv Math-phys 0802. 0402

      Pages: 1-15

    • Related Report
      2008 Annual Research Report
  • [Journal Article] A note on the nonrelativistic limit of Dirac operators and spectral concentration2007

    • Author(s)
      伊藤宏・山田修宣
    • Journal Title

      京都大学数理解析研究所講究録 1563

      Pages: 162-171

    • NAID

      40007140162

    • Related Report
      2009 Final Research Report
  • [Journal Article] Monotone operator functions, gaps and power moment problem2007

    • Author(s)
      H. Osaka, S. Silvestrov, J. Tomiyama
    • Journal Title

      Mathematica Scandinavica 100

      Pages: 161-183

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stable rank of depth two inclusion of $C^*$-algebras2007

    • Author(s)
      H. Osaka, T. Teruya
    • Journal Title

      C.R. Math. Acad. Sci. Soc. R. Canada 29

      Pages: 28-32

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] S. Silvestrov and J. Tomiyama, Monotone operator functions, gaps and power moment problem2007

    • Author(s)
      H. Osaka
    • Journal Title

      Mathematica Scandinavica 100

      Pages: 161-183

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] A note on the nonrelativistic of Dirac operators and spectral concentration2007

    • Author(s)
      伊藤 宏・山田 修宣
    • Journal Title

      数理解析研究所講究録 1563

      Pages: 162-171

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Monotone operator functions,gaps and Power moment problem2007

    • Author(s)
      H.Osaka, S.Silvestrov and J.Tomiyama
    • Journal Title

      Mathematica Scandinavica 100

      Pages: 161-183

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Stable rank of depth two inclusions of C*-algebras2007

    • Author(s)
      H.Osaka and T.Tamotsu
    • Journal Title

      C.R.Math.Acad.Sci.Soc.R.Can. 29

      Pages: 28-32

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Spectral analysis of radial Dirac operators in the Kerr-Newman metric and its applications to time-periodic solutions2006

    • Author(s)
      O. Yamada, M. Winklmeier
    • Journal Title

      J. Math. Phys. 47

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Furstenberg transformations on irrational rotation algebras2006

    • Author(s)
      H. Osaka, N.C. Phillips
    • Journal Title

      Ergodic Theory Dynamic Systems 26

      Pages: 1623-1651

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stable and real rank for crossed products by automorphisms with the tracial Rokhlin property2006

    • Author(s)
      H. Osaka, N.C. Phillips
    • Journal Title

      Ergodic Theory Dynamic Systems 26

      Pages: 1679-1621

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Topological stable rank of inclusions of unital $C^*$-algebras2006

    • Author(s)
      H. Osaka, T. Teruya
    • Journal Title

      Internet J. Math. 17

      Pages: 19-34

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] ディラック作用素のスペクトルについての一注意2006

    • Author(s)
      大鍛治隆司
    • Journal Title

      京都大学数理解析研究所講究録 1479

      Pages: 119-129

    • Related Report
      2009 Final Research Report
  • [Journal Article] On solutions of Wilson's functional equation on $R^2$2006

    • Author(s)
      M. Arai, H. Shin'ya, H.
    • Journal Title

      Mem. Inst. Sci. Engrg. Ritsumeikan Univ. 65

      Pages: 41-49

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semiclassical analysis for magnetic scattering by two solenoidal fields2006

    • Author(s)
      H.T. Ito, H. Tamura
    • Journal Title

      J. London Math. Soc. 74

      Pages: 695-716

    • Related Report
      2009 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectral analysis of radial Dirac operators in the Spectralanalysis of radial Dirac operators in theKerr-Newman metric and its applicationto time-periodic solutions2006

    • Author(s)
      M.Winklmeier and O.Yamada
    • Journal Title

      J.Math.Phys. 47

    • Related Report
      2008 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On solutions of Wilson's functional equations, Memoirs Inst.Sci.Engi.2006

    • Author(s)
      M. Arai and Shin' ya
    • Journal Title

      Ritsumeikan Univ. 66

      Pages: 41-49

    • Related Report
      2008 Self-evaluation Report
  • [Journal Article] Spectral analysis of radial Dirac operators in the Kerr-Newmann metric and its applications to time-periodic solutions2006

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

      J.Math.Phys. 47

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Furstenberg transformations on irrational rotation algebras2006

    • Author(s)
      Osaka, Hiroyuki, Phillips.N.Christopher
    • Journal Title

      Ergodic Theory Dynam.Systems 26

      Pages: 1623-1651

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Stable and real rank for crossed products by automorphisms with the tracial Rokhlin property2006

    • Author(s)
      Osaka, Hiroyuki, Phillips.N.Christopher
    • Journal Title

      Ergodic Theory Dynam.Systems 26

      Pages: 1579-1621

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Topological stable rank of inclusions of unital $Csp *$-algebras.2006

    • Author(s)
      Osaka, Hiroyuki, Teruya, Tamotsu
    • Journal Title

      Internat.J.Math. 17

    • Related Report
      2006 Annual Research Report
  • [Journal Article] ディラック作用素のスペクトルについての一注意2006

    • Author(s)
      大鍛治 隆司
    • Journal Title

      京都大学数理解析研究所講究録 1479

      Pages: 119-129

    • Related Report
      2006 Annual Research Report
  • [Presentation] Dirac operators with dilation analytic potentials diverging at infinity (with H.T. Ito2009

    • Author(s)
      山田修宣
    • Organizer
      XVI International Congress on Mathematical Physics
    • Place of Presentation
      チェコ・プラハ
    • Year and Date
      2009-08-04
    • Related Report
      2009 Final Research Report
  • [Presentation] Dirac operators with dilation analytic potentials diverging at infinity(with H.T.Ito)2009

    • Author(s)
      山田修宣
    • Organizer
      XVI International Congress on Mathematical Physics
    • Place of Presentation
      チェコ・プラハ
    • Year and Date
      2009-08-04
    • Related Report
      2009 Annual Research Report
  • [Presentation] On the nonrelativistic limit of Dirac operators with potentials diverging at infinity2008

    • Author(s)
      伊藤宏・山田修宣
    • Organizer
      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
      2008-12-05
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] On the nonrelativistic limit of Dirac operators with potentials diverging at infinity2008

    • Author(s)
      伊藤宏, 山田修宣
    • Organizer
      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
      2008-12-05
    • Related Report
      2008 Annual Research Report
  • [Presentation] Dirac作用素の非相対論的極限について2008

    • Author(s)
      伊藤宏・山田修宣
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-26
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] Dirac 作用素の非相対論的極限について2008

    • Author(s)
      伊藤宏, 山田修宣
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Spectral analysis of Dirac equations in the Kerr-Newman metric and its applications2008

    • Author(s)
      M. Winklmeier・山田修宣
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Year and Date
      2008-03-25
    • Related Report
      2009 Final Research Report 2008 Self-evaluation Report
  • [Presentation] Spectral analysis of Dirac equations in the Kerr-Newman metric and Its applications2008

    • Author(s)
      O.Yamada and M.Winklmeier
    • Organizer
      日本数学会・年会
    • Place of Presentation
      近畿大学本部キャンパス
    • Year and Date
      2008-03-25
    • Related Report
      2007 Annual Research Report
  • [Presentation] A note on the nonrelativistic limit of Dirac operators and spectral concentration2007

    • Author(s)
      伊藤宏・山田修宣
    • Organizer
      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
      2007-02-07
    • Related Report
      2009 Final Research Report
  • [Presentation] The nonreltivistic limit of Dirac operators and spectral concentration (with H.T. Ito)2006

    • Author(s)
      O. Yamada
    • Organizer
      Operator Theory in Quantum Physics
    • Place of Presentation
      チェコ・プラハ
    • Year and Date
      2006-09-11
    • Related Report
      2009 Final Research Report
  • [Presentation] ディラック作用素のスペクトルについて2006

    • Author(s)
      大鍛治隆司・山田修宣
    • Organizer
      第45回実函数論・函数解析学合同シンポジウム
    • Place of Presentation
      東海大学
    • Year and Date
      2006-08-09
    • Related Report
      2009 Final Research Report
  • [Presentation] ディラック作用素のスペクトルについてI2006

    • Author(s)
      山田修宣
    • Organizer
      第45回実函数論・函数解析学合同シンポジウム
    • Place of Presentation
      東海大学
    • Year and Date
      2006-08-09
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] ディラック作用素のスペクトルについてII2006

    • Author(s)
      大鍛治隆司
    • Organizer
      第45回実函数論・函数解析学合同シンポジウム
    • Place of Presentation
      東海大学
    • Year and Date
      2006-08-09
    • Related Report
      2008 Self-evaluation Report
  • [Presentation] A note on the essential selfadjointness of Dirac operators with an anomalous magnetic moment

    • Author(s)
      H. Kalf, T. Okaji, O. Yamada
    • Organizer
      第16回超局所解析と古典解析研究集会
    • Place of Presentation
      兵庫県竹野
    • Related Report
      2009 Final Research Report
  • [Book] A note on the nonrelativistic limit of Dirac operators and spectral concentration2007

    • Author(s)
      伊藤宏・山田修宣
    • Publisher
      京都大学数理解析研究所講究録1563
    • Related Report
      2008 Self-evaluation Report
  • [Book] 理工系微分積分学2006

    • Author(s)
      荒井正治
    • Total Pages
      251
    • Publisher
      学術図書出版
    • Related Report
      2009 Final Research Report
  • [Book] ディラック作用素のスペクトルについての一注意2006

    • Author(s)
      大鍛治隆司
    • Publisher
      京都大学数理解析研究所講究録1479
    • Related Report
      2008 Self-evaluation Report
  • [Book] 理工系微分積分学2006

    • Author(s)
      荒井正治
    • Total Pages
      251
    • Publisher
      学術図書
    • Related Report
      2008 Self-evaluation Report
  • [Book] 理工系 微分積分学2006

    • Author(s)
      荒井 正治
    • Total Pages
      251
    • Publisher
      学術図書出版
    • Related Report
      2006 Annual Research Report
  • [Remarks]

    • URL

      http://xxx.lanl.gov/abs/0802.0402

    • Related Report
      2008 Annual Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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