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Analysis of Schrodinger operators with random δ magnetic fields

Research Project

Project/Area Number 20740093
Research Category

Grant-in-Aid for Young Scientists (B)

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

Principal Investigator

MINE Takuya  Kyoto Institute of Technology, 工芸科学研究科, 准教授 (90378597)

Research Collaborator NOMURA Yuji  愛媛大学, 大学院・理工学研究科, 准教授 (40282818)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords解析学 / 関数解析学 / 関数方程式論 / 数理物理
Research Abstract

We give the range of the spectrum of the Schrodinger operators with random delta magnetic fields of the Anderson type, or of the Poisson type, and estimate the degeneracy of the Landau levels. We prove the Lifshitz tail for the Anderson case. We also study the Schrodinger operators with delta magnetic fields on the Poincare upper half plane, and estimate the number of eigenvalues in Landau gaps for finite delta fields, and the degeneracy of the Landau levels for the lattice case.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (29 results)

All 2011 2010 2009 2008

All Journal Article (14 results) (of which Peer Reviewed: 11 results) Presentation (15 results)

  • [Journal Article] Self-adjoint extensions of Schrodinger operators withδ-magnetic fields on Riemannian manifolds2010

    • Author(s)
      Takuya Mine
    • Journal Title

      Acta Polytechnica Vol.50, No.5

      Pages: 62-72

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The spectrum of Schrodinger operators with periodic Aharonov-Bohm magnetic fields2010

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

      RIMS kokyuroku Bessatsu B16

      Pages: 135-140

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Spectral properties of Schrodinger operators with singular magnetic fields supported by a circle in R^32010

    • Author(s)
      岩塚明, 峯拓矢, 島田伸一
    • Journal Title

      数理解析研究所講究録スペクトル・散乱理論とその周辺 1696

      Pages: 79-93

    • Related Report
      2010 Final Research Report
  • [Journal Article] Self-adjoint Extensions of Schrodinger Operators with delta-magnetic Fields on Riemannian Manifolds2010

    • Author(s)
      Takuya Mine
    • Journal Title

      Acta Polytechnica

      Volume: Vol.50, No.5 Pages: 62-72

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The spectrum of Schrodinger Operators operators with periodic Aharonov-Bohm magnetic fields2010

    • Author(s)
      峯拓矢, 野村祐司
    • Journal Title

      数理解析研究所講究録別冊

      Volume: B16 Pages: 135-140

    • Related Report
      2010 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 Systems, P.Briet, F.Germinet and G. Raikov (Ed.)2009

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

      Contemporary Mathematics 500, AMS

      Pages: 139-151

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The spectrum of Schrodinger operators with random δmagnetic fields2009

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

      Annales de l'Institut Fourier 59 No.2

      Pages: 659-689

    • NAID

      120006524900

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The spectrum of Schrodinger operators with random delta magnetic fields2009

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

      Annales de l'Institute Fourier 59

      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, Takuya Mine, Shin-ichi Shimada
    • Journal Title

      Contemporary Mathematics 500

      Pages: 139-151

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The spectrum of Schrodinger operators with random δ magnetic fields2009

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

      Annales de l' Institut Fourier 59(掲載決定済)

    • NAID

      120006524900

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Schrodinger Operators with RandomδMagnetic Fields, MATHEMATICAL RESULTS IN QUANTUM MECHANICS, Proceedings of the QMath10 Conference (edited by Ingrid Beltita, Gheorghe Nenciu and Radu Purice)2008

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

      World Scientific

      Pages: 203-217

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Schrodinger operators with random δ magnetic fields2008

    • Author(s)
      野村祐司, 峯拓矢
    • Journal Title

      数理解析研究所講究録スペクトル・散乱理論とその周辺 1607

    • Related Report
      2010 Final Research Report
  • [Journal Article] Schrodinger operators with random δ magnetic fields2008

    • Author(s)
      峯拓矢、野村祐司
    • Journal Title

      スペクトル・散乱理論とその周辺RIMS研究集会報告集 1607

      Pages: 1-8

    • Related Report
      2008 Annual Research Report
  • [Journal Article] Schrodinger operators with random δ magnetic fields2008

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

      Mathematical Results in Quantum Mechanics : Pro ceedings of the Qmath10 Conference, 10-15 September 2007

      Pages: 203-217

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] Yuji Nomuraとの共同研究2011

    • Author(s)
      Takuya Mine
    • Organizer
      The spectrum of the Aharonov-Bohm Hamiltonian on the hyperbolic plane, Spectral and Scattering Theory and Related Topics
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2011-02-17
    • Related Report
      2010 Final Research Report
  • [Presentation] The spectrum of the Aharonov-Bohm Hamiltonian on the hyperbolic plane2011

    • Author(s)
      Takuya Mine, Yuji Nomura
    • Organizer
      Spectral and Scattering Theory and Related Topics
    • Place of Presentation
      RIMS, Kyoto(招待講演)
    • Year and Date
      2011-02-17
    • Related Report
      2010 Annual Research Report
  • [Presentation] Self-adjoint extensions of the Aharonov-Bohm Hamiltonian on Riemannian manifolds2010

    • Author(s)
      Takuya Mine
    • Organizer
      Qmath 11 Mathematical Results in Quantum Physics
    • Place of Presentation
      University of Hradec Kralove (Hradec Kralove, Czech Republic)
    • Year and Date
      2010-09-08
    • Related Report
      2010 Final Research Report
  • [Presentation] Self-adjoint extensions of the Aharonov-Bohm Hamiltonian on Riemannian manifolds2010

    • Author(s)
      Takuya Mine
    • Organizer
      QMath11 Mathematical Results in Quantum Physics
    • Place of Presentation
      Hradec Kralove, Czech republic
    • Year and Date
      2010-09-08
    • Related Report
      2010 Annual Research Report
  • [Presentation] 双曲平面におけるAharonov-Casher型定理について2010

    • Author(s)
      峯拓矢
    • Organizer
      準古典解析における諸問題
    • Place of Presentation
      京都大学数理解析研究所(京都市左京区)
    • Year and Date
      2010-07-06
    • Related Report
      2010 Final Research Report
  • [Presentation] Lifshitz Tail for Schrodinger Operators with Random δMagnetic Fields2010

    • Author(s)
      Takuya Mine
    • Organizer
      Arizona School of Analysis with Applications
    • Place of Presentation
      University of Arizona (Tucson, United States)
    • Year and Date
      2010-03-16
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectrum of the Aharonov-Bohm Hamiltonian with constant magnetic fields in the hyperbolic plane2010

    • Author(s)
      Takuya Mine
    • Organizer
      CSASC 2010
    • Place of Presentation
      Charles University (Prague, Czech republic)
    • Year and Date
      2010-01-22
    • Related Report
      2010 Final Research Report
  • [Presentation] Spectrum of the Aharonov-Bohm Hamiltonian with constant magnetic fields in the hyperbolic plane2010

    • Author(s)
      Takuya Mine
    • Organizer
      CSASC2010(招待講演)
    • Place of Presentation
      Prague, Czech Republic
    • Year and Date
      2010-01-22
    • Related Report
      2009 Annual Research Report
  • [Presentation] Aharonov-Bohm Solenoids in a homogeneous magnetic field (ポスター発表)2009

    • Author(s)
      Takuya Mine
    • Organizer
      Aharonov-Bohm Effect and Berry Phase Anniversary 50/25
    • Place of Presentation
      University of Bristol(Bristol, England)
    • Year and Date
      2009-12-15
    • Related Report
      2010 Final Research Report
  • [Presentation] Aharonov-Bohm Solenoids on the Hyperbolic Plane2009

    • Author(s)
      Takuya Mine, Yuji Nomura
    • Organizer
      XVI International Congress on Mathematical Physics
    • Place of Presentation
      Prague, Czech Republic
    • Year and Date
      2009-08-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] Aharonov-Bohm Solenoids on the Hyperbolic Plane2009

    • Author(s)
      Takuya Mine
    • Organizer
      XVI International Congress on Mathematical Physics
    • Place of Presentation
      Clarion Congress Hotel Prague(Prague, Czech Republic)
    • Year and Date
      2009-08-01
    • Related Report
      2010 Final Research Report
  • [Presentation] Norm resolvent convergence to Schrodinger operators with infinitesimally thin toroidal magnetic fields2009

    • Author(s)
      Takuya Mine
    • Organizer
      Analytic and algebraic methods in physics V
    • Place of Presentation
      Villa Lanna(Prague, Czech Republic)
    • Year and Date
      2009-05-27
    • Related Report
      2010 Final Research Report
  • [Presentation] ランダムδ磁場におけるリフシッツ・テイルについて2008

    • Author(s)
      Takuya Mine
    • Organizer
      2008年度日本数学会秋季総合分科会
    • Place of Presentation
      東京工業大学(東京都目黒区)
    • Year and Date
      2008-09-26
    • Related Report
      2010 Final Research Report
  • [Presentation] ランダムδ磁場におけるリフシッツテイルについて2008

    • Author(s)
      峯拓矢、野村祐司
    • Organizer
      日本数学会・2008年度秋季総合分科会
    • Place of Presentation
      東京工業大学
    • Year and Date
      2008-09-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] Norm resolvent convergence to Schrodinger operators with infinitesimally thin toroidal magnetic fields2008

    • Author(s)
      Takuya Mine
    • Organizer
      Spectral and Scattering Theory for Quantum Magnetic Systems
    • Place of Presentation
      Centre International de Rencontres Math'ematiques(Luminy, France)
    • Year and Date
      2008-07-08
    • Related Report
      2010 Final Research Report

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Published: 2008-04-01   Modified: 2016-04-21  

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