• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Studies on Spectral Structure of Shrodinger Operators with Electromagnetic Fields

Research Project

Project/Area Number 10640204
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  Faculty of Textile Science, KYOTO INSTITUTE OF TECHNOLOGY Professor, 繊維学部, 教授 (40184890)

Co-Investigator(Kenkyū-buntansha) DOI Shin-ichi  Institute of Mathematics, University of Tsukuba, Associate Professor, 数学系, 助教授 (00243006)
YAGASAKI Tatsuhiko  Faculty of Engineering and Design, KYOTO INSTITUTE OF TECHNOLOGY Associate Professor, 工芸学部, 助教授 (40191077)
UCHIYAMA Jun  Faculty of Textile Science, KYOTO INSTITUTE OF TECHNOLOGY Professor, 繊維学部, 教授 (70025401)
SHIMADA Shin-ichi  Department of Mathematics and Physics, Setsunan University, Associate Professor, 工学部, 助教授 (40196481)
ITO Hiroshi  Faculty of Engineering, Ehime University, Associate Professor, 工学部, 助教授 (90243005)
Project Period (FY) 1998 – 1999
Project Status Completed (Fiscal Year 1999)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 1999: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 1998: ¥1,800,000 (Direct Cost: ¥1,800,000)
KeywordsSchrodinger Operator / Periodic Electromagnetic Field / Spectral Structure / Magnetic Field / Selfadjoint Extention / Aharonov-Bohm Effect / Density of States / Wavefunction / シュレディンガー作用素 / 周期的ポテンシャル
Research Abstract

To begin with, we studied the Schrodinger operators with point interactions with Shin-ichi Shimada. Namely we studied the Schrodinger operator with a magnetic point interaction at the origin known as Aharonov-Bohm effect Hamiltonian. Since this operator defined on the space of compactly supported smooth functions is not essentially selfadjoint, w determined all the self adjoint extension of this operator and their boundary conditions at the origin. We also showed that one can calculate the asymptotic completeness, the phase shift formula, the eigenfunction expansions etc. for these operators which preserves the angular momentum. We obtained expressions of the wave operators, scattering matrices and the scattering amplitudes, and showed the eigenfunction expansion formula as well. This enabled to characterize the operator treated by Aharonov and Bohm in terms of the behavior at the origin of the wavefunctions.
We also studied on the uniqueness of the integrated density of states with Shin-ichi Doi. We showed that the integrated density of states is uniquely defined independently of the way to extend the regions to the whole space or the choisce of the boundary conditions under relatively general assumptions in the presence of the magnetic fields. Also we obtained a sufficient conditions for the coincidence of the integrated density of states defined in terms of the whole space operator and that defined by using the finite region operators. This enabled to compute the spectrum of the whole space operators by calculating those of the finite region operators.

Report

(3 results)
  • 1999 Annual Research Report   Final Research Report Summary
  • 1998 Annual Research Report
  • Research Products

    (23 results)

All Other

All Publications (23 results)

  • [Publications] 岩塚 明: "Asymptootic distribution of eigenvalues for Pauli operators with nonconstant magnetic fields"Duke Mathematical Jouranal. 93-3. 535-574 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 岩塚 明: "Asymptootic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields"Annales de l'Institut Fourier. 48-2. 479-515 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 内山 淳: "On the von Neumann and Wigner Potentials"Journal of Differential Equations. 157. 348-372 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 矢ケ崎達彦: "The groups of quasiconformal homeomorphisms on Riemann surfaces"Proceedeings of the American Mathematical Society. 127-9. 2727-2734 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 土居伸一: "Commutator algebra and abstract smoothing effect"Journal of Functional Analysis. 168-2. 428-469 (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 伊藤 宏: "An inverse scattering problem for Dirac equations with time-dependent electromagnetic potentials"Publications of the Research Institute for Mathematical Sciences, Kyoto University. 34. 335-381 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. Iwatsuka and H. Tamura: "Asymptotic distribution of eigenval-ues for Pauli operators with nonconstant magnetic fields"Duke Mathematical Journal. 93-3. 535-574 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] A. Iwatsuka and H. Tamura: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields"Annales de l'Institut Fourier. 48-2. 479-515 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] M. Arai and J. Uchiyama: "On the von Neumann and Wiegner Potentials"Journal of Differential Equa-tions. 157. 348-372 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] T. Yagasaki: "The groups of quasiconformal homeomorphisms on Riemann surfaces"Proceedings of the American Mathematical Society. 127-9. 2727-2734 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] S.Doi: "Commutator algebra and abstract smoothing effect"Journal of Functional Analysis. 168-2. 428-469 (1999)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] H Ito: "An inverse scattering problem for Dirac equations with time-dependent electromagnetic potentials"Publications of the Research In-stitute for Mathematical Sci-ences, Kyoto University. 34. 355-381 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1999 Final Research Report Summary
  • [Publications] 岩塚 明: "Asymptotic distribution of eigenvalues for Pauli operators with nonconstant magnetic fields"Duke Mathematical Journal. 93-3. 535-574 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 岩塚 明: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields"Annales de l'Institut Fourier. 48-2. 479-515 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 内山 淳: "On the von Neumann and Wiegner Potentials"Journal of Differential Equations. 157. 348-372 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 矢ケ崎達彦: "The groups of quasiconformal homeomorphisms of Riemann surfaces"Proceedings of the American Mathematical Society. 127-9. 2727-2734 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 土居伸一: "Commutator algebra and abstract smoothing effect"Journal of Functional Analysis. 168-2. 428-469 (1999)

    • Related Report
      1999 Annual Research Report
  • [Publications] 伊藤 宏: "An inverse scattering problem for Dirac equations with time-dependent electromagnetic potentials"Publications of the Research Institute for Mathematical Sciences,Kyoto University. 34. 355-381 (1998)

    • Related Report
      1999 Annual Research Report
  • [Publications] 岩塚 明: "Asymptotic distribution of eigenvalues for Pauli operators with spherically symmetric magnetic fields" Tsukuba Journal of Mathematics. 22-2. 281-303 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 岩塚 明: "Asymptotic distribution of eigenvalues for Pauli operators with nonconstant magnetic fields" Duke Mathematical Journal. 93-3. 535-573 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 岩塚 明: "Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields" Annales de l'Institut Fourier. 48-2. 479-515 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 伊藤 宏: "An inverse scattering problem for Dirac equations with time-dependent electromagnetic potentials" Publications of the Research Institute for Mathematical Sciences,Kyoto University. 34. 355-381 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 矢ヶ崎 達彦: "The groups of quasiconformal homeomorphisms on Riemann surfaces" Proceedings of the American Mathematical Society. (印刷中).

    • Related Report
      1998 Annual Research Report

URL: 

Published: 1998-04-01   Modified: 2016-04-21  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi