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2008 Fiscal Year Final Research Report

Study of the spectrum of the Pauli and Dirac operators with singular magnetic field

Research Project

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Project/Area Number 18540215
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionKyoto Institute of Technology

Principal Investigator

IWATSUKA Akira  Kyoto Institute of Technology, 工芸科学研究科, 教授 (40184890)

Co-Investigator(Renkei-kenkyūsha) TAMURA HIDEO  岡山大学, 自然科学研究科, 教授 (30022734)
MINE TAKUYA  京都工芸繊維大学, 工芸科学研究科, 准教授 (90378597)
OKAJI TAKASHI  京都大学, 理学研究科, 准教授 (20160426)
YAMADA OSANOBU  立命館大学, 理工学部, 教授 (70066744)
SHIMADA SHINICHI  摂南大学, 工学部, 准教授 (40196481)
Project Period (FY) 2006 – 2008
Keywords関数解析学 / 関数方程式論 / 数理物理 / スペクトル理論 / 散乱理論
Research Abstract

3次元空間におけるトーラス内に台をもつ磁場をもつシュレディンガー作用素が, トーラスの厚みを薄くしたときに, 磁場のベクトルポテンシャルをうまく選ぶことにより, 特異性をもつ磁場をもつシュレディンガー作用素のフリードリックス拡張で定まる自己共役作用素にノルムレゾルベントの意味で収束することを示した。

  • Research Products

    (16 results)

All 2009 2008 2007 2006

All Journal Article (11 results) (of which Peer Reviewed: 10 results) Presentation (5 results)

  • [Journal Article] The spectrum of Schroedinger operators with random delta magnetic fields2009

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

      Annales de l'Institut Fourier 59-2

      Pages: 659-689

    • Peer Reviewed
  • [Journal Article] Schroedinger operators with random delta magnetic fields, Mathematical Results in Quantum Mechanics2008

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

      Proceedings of the QMath 10 Conference, World Scientific

      Pages: 203-217

    • Peer Reviewed
  • [Journal Article] Semiclassical analysis for spectral shift functions in magnetic scattering by two solenoidal fields2008

    • Author(s)
      Hideo Tamura
    • Journal Title

      Rev. Math. Phys 20

      Pages: 1249-1282

    • Peer Reviewed
  • [Journal Article] Time delay in scattering by potentials and by magnetic fields with two supports at large separation2008

    • Author(s)
      Hideo Tamura
    • Journal Title

      J.Funct. Anal 254

      Pages: 1735-1775

    • Peer Reviewed
  • [Journal Article] Semiclassical analysis for magnetic scattering by two solenoidal fields : total cross sections2007

    • Author(s)
      Hideo Tamura
    • Journal Title

      Ann. Henri Poincare 8

      Pages: 1071-1114

    • Peer Reviewed
  • [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

      数理解析研究所講究録1563「スペクトル散乱理論とその周辺」

      Pages: 162-171

  • [Journal Article] The spectrum of Schroedinger operators with Poisson type random potential2006

    • Author(s)
      Kazunori Ando, Akira Iwatsuka, Masahiro Kaminaga, Fumihiko Nakano
    • Journal Title

      Ann. Henri Poincare 7-1

      Pages: 145-160

    • Peer Reviewed
  • [Journal Article] Periodic Aharonov-Bohm solenoids in a constant magnetic field2006

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

      Rev. Math. Phys 47-10

      Pages: 913-934

    • Peer Reviewed
  • [Journal Article] Spectral analysis of radial Dirac operators in the Kerr-Neuman metric and its applications to time periodic solutions2006

    • Author(s)
      Monica Winklemeier, Osanobu Yamada
    • Journal Title

      J.Math. Phys 47-10

      Pages: 1-17

    • Peer Reviewed
  • [Journal Article] Semiclassical analysis for magnetic scattering by two solenoidal fields2006

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

      J.London Math. Soc. 8

      Pages: 695-716

    • Peer Reviewed
  • [Journal Article] Exponential product approximation to the integral kernel of te Schroedinger semigroup and to the heat kernel of the Dirichlet Laplacian2006

    • Author(s)
      Takashi Ichinose, Hideo Tamura
    • Journal Title

      J.Reine Angew. Math. 8

      Pages: 695-716

    • Peer Reviewed
  • [Presentation] 磁場散乱におけるアハラノフ・ボーム効果に対する純子点漸近解析2009

    • Author(s)
      田村英男
    • Organizer
      日本数学会2009年度年会特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
  • [Presentation] Norm resolvent convergence to Schroedinger oerators with singular magnetic fields supported by a circle in R^32009

    • Author(s)
      Akira Iwatsuka
    • Organizer
      Schroedinger Equation an Related Topics
    • Place of Presentation
      東京大学数理科学研究科
    • Year and Date
      2009-01-06
  • [Presentation] On the nonrelativistic limit of Dirac 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
  • [Presentation] Norm resolvent convergence of to Schroedinger operators with infinitesimally thin toroidal magnetic fields2008

    • Author(s)
      Takuya Mine
    • Organizer
      Spectral and Scattering Theory for Quantum Magnetic Systems
    • Place of Presentation
      CIRM, Marseille, France
    • Year and Date
      2008-07-08
  • [Presentation] Schroedinger operators with random delta magnetic fields2007

    • Author(s)
      Takuya Mine
    • Organizer
      10^<th> Quantum Mathematics International Conference
    • Place of Presentation
      Moeciu, Romania
    • Year and Date
      2007-12-12

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Published: 2010-06-10   Modified: 2016-04-21  

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