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

2002 Fiscal Year Final Research Report Summary

Scattering by magnetic fields and Aharonov-Bohm effect

Research Project

Project/Area Number 13640176
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionOKAYAMA UNIVERSITY

Principal Investigator

TAMURA Hideo  Okayama University Science Prof, 理学部, 教授 (30022734)

Co-Investigator(Kenkyū-buntansha) IWATSUKA Akira  Kyoto Institute of Technology Prof, 繊維学部, 教授 (40184890)
HIROKAWA Masao  Okayama University Science Assistant Prof, 理学部, 助教授 (70282788)
KATSUDA Atsushi  Okayama University Science Assistant Prof, 理学部, 助教授 (60183779)
ITO Hiroshi  Okayama University Engineering Assistant Prof, 工学部, 助教授 (90243005)
Project Period (FY) 2001 – 2002
Keywordsmagnetic Scchrodinger operator / Aharonov-Bohm effect / δ-like magnetic field / scattering arnplitude
Research Abstract

The present project has been devoted to the study on the scattering problem by several point-like magnetic fields in two dimensions. According to the Aharonov-Bohm effect, magnetic potentials have a direct significance to the motion of particles in quantum mechanics. We study this quantum effect through the scattering by several point-like magnetic fields at large separation in two dimensions. We derive the asymptotic formula for scattering amplitudes as the distances between centers of fields go to infinity. A special emphasis is placed on the case of scattering by fields with centers on an even line. The obtained result depends on fluxes of fields and on ratios of distances between adjacent centers. We figure the approximate values obtained from the asymptotic formula for the differential cross sections and we see how the pattern of interferences changes with flux parameters.

  • Research Products

    (14 results)

All Other

All Publications (14 results)

  • [Publications] 田村 英男: "Norm resolvent convergence to magnetic Schrodinger operators with point interactions"Rev.Math.Phys.. 13. 465-511 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤 宏, 田村 英男: "Aharonov-Bohm effect in scattering by point-like magnetic fields at large separation"Ann.Henri Poincare. 2. 309-359 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤 宏, 田村 英男: "Scattering by magnetic fields at large separation"Rubl.Res.Inst.Math.Sci.. 37. 531-578 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤 宏, 田村 英男: "Asymptotic behavior of scattering amplitudes in magnetic fields at large separation"J.Math.Soc. Japan. 53. 645-668 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 一瀬 孝, 田村 英男: "The norm convergence of the Trotter-Kato product formula with error bound"Commun.Math.Phys.. 217. 489-502 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 一瀬 孝, 田村 英男, 田村 博志, V.A.Zagrebnov: "Note on the paper "The norm convergence of the Trotter-Kato product formula with error bound" by T.Ichinose and H.Tamura"Commun.Math.Phys.. 221. 499-510 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 伊藤 宏, 田村 英男: "Aharanov-Bohm effect in scattering by a chain of point-like magnetic fields"Asymptot.Anal.. (in press). (2002)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H. Tamura: "Norm resolvent convergence to magnetic Schrodinger operators with point interactions"Rev. Math. Phys.. 13. 465-511 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. T. Ito and H. Tamura: "Aharonov-Bohm effect in scattering by point-like mag-netic fields at large separation"Ann. Henri Poincare. 2. 309-359 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. T. Ito and H. Tamura: "Scattering by magnetic fields at large separation, Rubl. Res."Inst Math. Sci.. 37. 531-578 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. T. Ito and H. Tamura: "Asymptotic behavior of scattering amplitudes in magnetic fields at large separation"J. Math. Soc. Japan. 53. 645-668 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Ichinose and Hideo Tamura: "The norm convergence of the Trotter-Kato product formula with error bound"Commun. Math. Phys.. 217. 489-502 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Takashi Ichinose, Hideo Tamura, Hiroshi Tamura and V. A. Zagrebnov: "Note on the paper "The norm convergence of the Trotter-Kato product formula with error bound" by T. Ichinose and H. Tarnura"Commun. Math. Phys.. 221. 499-510 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. T. Ito and H. Tamura: "Aharanov-Bohm effect in scattering by a chain of point-like magnetic fields"Asymptot. Anal, in press. 2002.

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 2004-04-14  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi