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Asymptotic Analysis in Spectral and Scattering Theory

Research Project

Project/Area Number 18340049
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Global analysis
Research InstitutionOkayama University

Principal Investigator

TAMURA Hideo  Okayama University, 大学院・自然科学研究科, 教授 (30022734)

Co-Investigator(Kenkyū-buntansha) HIROKAWA Masao  岡山大学, 大学院・自然科学研究科, 教授 (70282788)
KATSUDA Atsushi  岡山大学, 大学院・自然科学研究科, 准教授 (60183779)
ICHINOSE Takashi  金沢大学, 大学院・自然科学研究科, 名誉教授 (20024044)
IWATSUKA Akira  京都工芸繊維大学, 工芸科学研究科, 教授 (40184890)
ITO Hiroshi,t  愛媛大学, 大学院・理工学研究科, 教授 (90243005)
NAKNO Fumihiko  高知大学, 理学部, 准教授 (10291246)
MINE Takuya  京都工芸繊維大学, 工芸科学研究科, 准教授 (90378597)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥7,790,000 (Direct Cost: ¥6,500,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2008: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2006: ¥2,200,000 (Direct Cost: ¥2,200,000)
Keywords関数方程式の大域理論 / スペクトル散乱理論 / シュレディンガー作用素 / 準古典漸近解析 / アハラノフ・ボーム効果 / スペクトル理論 / 散乱理論 / アハラノフ・ポーム効果 / 磁場散乱 / 散乱全断面積 / 散乱位相 / 準古典近似 / 散乱振幅 / ソレノイド磁場 / 準古典漸近公式 / 指数積近似 / 熱核
Research Abstract

量子力学が提供する数学の諸問題は広く深く、そして豊かである。その研究対象であるミクロな世界では古典力学的な観点から説明できない注目すべき現象がしばしば生じる。このような自然現象は量子効果とよばれ、ひとつひとつが数学解析の格好の題材を提供している。本研究は、スペクトル理論において培われた漸近的手法を駆使し、量子力学に現れる量子効果のいくつかについて、その数理現象を追究する目的で行われた研究である。とくに、複数個のソレノイド磁場による散乱におけるアハラノフ・ボーム量子効果について準古典漸近解析を展開した

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (29 results)

All 2009 2008 2007 2006

All Journal Article (14 results) (of which Peer Reviewed: 10 results) Presentation (15 results)

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

    • Author(s)
      H. Tamura
    • Journal Title

      Rev. Math. Phys 20

      Pages: 1249-1282

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Time delay in scattering by potentials and by magnetic fields with two supports at large separation2008

    • Author(s)
      H. Tamura
    • Journal Title

      J. Func. Anal 254

      Pages: 1735-1775

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Time delay in scattering by potentials and by magnetic fields with two supports at large separation2008

    • Author(s)
      田村 英男
    • Journal Title

      J. Func. Anal. 254

      Pages: 1736-1775

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semiclassical analysis for spectral shift functions in magnetic scattering by two solenoidal fields2008

    • Author(s)
      田村 英男
    • Journal Title

      Rev. Math. Phys. 20

      Pages: 1249-1282

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Time delay in scattering by potentials and by magnetic fields with two supports at large separation2008

    • Author(s)
      田村 英男
    • Journal Title

      J. Func. Anal.(掲載決定(校正済))

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Note on norm and pointwise convergence of exponential productsand their integral kernels for the harmonic oscillator2008

    • Author(s)
      一瀬 孝, (他1名).
    • Journal Title

      Integral Equations Operator Theory(掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semiclassical analysis for magnetic scattering by two solenoidal fields : total cross sections2007

    • Author(s)
      H. Tamura
    • Journal Title

      Ann. Henri Poincare 8

      Pages: 1071-1114

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Semiclassical analysis for magnetic scattering by two solenoidal fields: Total cross sections2007

    • Author(s)
      田村 英男
    • Journal Title

      Ann. Henri. Poincare 8

      Pages: 1071-1114

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Semiclassical analysis for magnetic scattering by two solenoidal fields : total cross sections2007

    • Author(s)
      田村 英男
    • Journal Title

      Ann. H. Poincare (掲載決定(校正済)(確約あり))

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Semiclassical analysis for magnetic scattering by two solenoidal fields2006

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

      J. London Math. Soc 74

      Pages: 695-716

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exponential product approximation to the integral kernel of the Schrodinger semigroup and to the heat kernel of the Dirichlet Laplacian2006

    • Author(s)
      T. Ichinose and H. Tamura
    • Journal Title

      J. Reine Angew. Math. 592

      Pages: 157-188

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Exponential product approximation to integral kernel of Schroedinger semigroup and to heat kernel of Dirichlet Laplacian2006

    • Author(s)
      一瀬 孝, 田村 英男
    • Journal Title

      J. Reine Angew. Math. 592

      Pages: 157-188

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Semiclassical analysis for magnetic scattering by two solenoidal fields2006

    • Author(s)
      伊藤 宏, 田村 英男
    • Journal Title

      J. London Math. Soc. 74

      Pages: 695-716

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The spectrum of Schroedinger operators with Poisson type random potentials2006

    • Author(s)
      岩塚 明(他3名)
    • Journal Title

      Ann. H. Poincare 7

      Pages: 145-160

    • Related Report
      2006 Annual Research Report
  • [Presentation] 磁場散乱におけるアハラノフ・ホーム効果に対する準古典漸近解析2009

    • Author(s)
      田村 英男
    • Organizer
      日本数学会 函数方程式分科会 特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2009-03-26
    • Related Report
      2008 Annual Research Report
  • [Presentation] 磁場散乱におけるアハラノフ・ボーム効果に対する準古典漸近解析2009

    • Author(s)
      田村英男
    • Organizer
      日本数学会年会函数解析学分科会特別講演
    • Place of Presentation
      東京大学
    • Related Report
      2008 Final Research Report
  • [Presentation] Semiclassical analysis for spectral shift functions in magnetic scattering by two solenoidal fields2009

    • Author(s)
      田村英男
    • Organizer
      第19回「微分方程式と数理物理」研究集会
    • Place of Presentation
      静岡県熱海市
    • Related Report
      2008 Final Research Report
  • [Presentation] ポテンシャル散乱と磁場散乱におけるあるレゾナンス問題について2008

    • Author(s)
      田村英男
    • Organizer
      第15回「超局所解析と古典解析」研究集会
    • Place of Presentation
      福井県坂井市
    • Related Report
      2008 Final Research Report
  • [Presentation] Resonances in scattering by potential and by magnetic field with two supports at large separation2008

    • Author(s)
      田村英男
    • Organizer
      作用素論セミナー
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2008 Final Research Report
  • [Presentation] Semiclassical analysis for scattering by two magnetic fields ; spectral shift functions2008

    • Author(s)
      田村英男
    • Organizer
      作用素論セミナー
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2008 Final Research Report
  • [Presentation] Semiclassical analysis for scattering by two solenoidal fields2007

    • Author(s)
      田村 英男
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      東京大学
    • Year and Date
      2007-12-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] Semiclassical analysis for magnetic scattering by two solenoidal fields2007

    • Author(s)
      田村英男
    • Organizer
      微分方程式の総合的研究
    • Place of Presentation
      東京大学数理科学研究科
    • Related Report
      2008 Final Research Report
  • [Presentation] Spectral sfift function in magnetic scattering by two solenoidal fields2007

    • Author(s)
      田村英男
    • Organizer
      第18回「微分方程式と数理物理」研究集会
    • Place of Presentation
      山口県萩市
    • Related Report
      2008 Final Research Report
  • [Presentation] Time delay in scattering by potentials and by magnetic fields with two supports at large separation2007

    • Author(s)
      H. Tamura
    • Organizer
      Analysis Seminar, Nantes
    • Place of Presentation
      University, France
    • Related Report
      2008 Final Research Report
  • [Presentation] Time delay in scattering by potentials and by magnetic fields with two supports at large separation2007

    • Author(s)
      田村英男
    • Organizer
      作用素論セミナー
    • Place of Presentation
      兵庫県立大学神戸キャンパス
    • Related Report
      2008 Final Research Report
  • [Presentation] ソレノイド磁場による散乱におけるレゾナンスについて2006

    • Author(s)
      田村英男
    • Organizer
      第13回「超局所解析と古典解析」研究集会
    • Place of Presentation
      岐阜県郡上市
    • Related Report
      2008 Final Research Report
  • [Presentation] Aharonov-Bohm effect in scattering by two solenoidal fields2006

    • Author(s)
      田村英男
    • Organizer
      Recent Topics on Differential Equations
    • Place of Presentation
      群馬大学東京オフフィス
    • Related Report
      2008 Final Research Report
  • [Presentation] Semiclassical analysis for magnetic scattering by two solenoidal fields ; total cross sections2006

    • Author(s)
      田村英男
    • Organizer
      作用素論セミナー
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2008 Final Research Report
  • [Presentation] Semiclassical analysis for magnetic scattering by two solenoidal fields2006

    • Author(s)
      H. Tamura
    • Organizer
      Spectral Analysis in Mathematical Physics
    • Place of Presentation
      Nantes University, France
    • Related Report
      2008 Final Research Report

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

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