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

2011 Fiscal Year Final Research Report

Semi-classical Analysis for Schrodinger Equations

Research Project

  • PDF
Project/Area Number 21540195
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionRitsumeikan University (2010-2011)
University of Hyogo (2009)

Principal Investigator

FUJIIE Setsuro  立命館大学, 理工学部, 教授 (00238536)

Co-Investigator(Renkei-kenkyūsha) HOSHIRO Toshihiko  兵庫県立大学, 大学院・物質理学研究科, 教授 (40211544)
UMEDA Tomio  兵庫県立大学, 大学院・物質理学研究科, 教授 (20160319)
IWASAKI Chisato  兵庫県立大学, 大学院・物質理学研究科, 教授 (30028261)
DOI Shinichi  大阪大学, 大学院・理学研究科, 教授 (00243006)
WATANABE Takuya  立命館大学, 理工学部, 助教 (80458009)
Project Period (FY) 2009 – 2011
Keywords準古典解析 / シュレディンガー方程式
Research Abstract

We consider the scattering problem for Schrodinger equations. If the corresponding classical dynamics has trapped trajectories at an energy, some complex poles of the resolvent, called resonances, appear near this energy. We have succeeded in clarifying the semiclassical distribution etc. of resonances near the potential (1) minimum, (2) maximum and (3) the conical intersection in the case of a system.

  • Research Products

    (15 results)

All 2011 2010 2009

All Journal Article (9 results) (of which Peer Reviewed: 9 results) Presentation (6 results)

  • [Journal Article] Spectral projection, residue of the scattering amplitude and Schrodinger group expansion for barrier-top resonances2011

    • Author(s)
      J. F. Bony, S. Fujiie, T. Ramond, M. Zerzeri
    • Journal Title

      Ann. Inst. Fourier, Grenoble

      Volume: 61-4 Pages: 1351-1406

    • Peer Reviewed
  • [Journal Article] Width of shape resonances for non globally analytic potentials2011

    • Author(s)
      S. Fujiie, A. Lahmar-Benbernou, A. Martinez
    • Journal Title

      J. Math. Soc. Japan

      Volume: 63 Pages: 1-78

    • Peer Reviewed
  • [Journal Article] Calculus of pseudo-differential operators and a local index of Dirac operators2011

    • Author(s)
      C. Iwasaki
    • Journal Title

      Oper. Thoery Adv. Appl.

      Volume: 213 Pages: 123-136

    • Peer Reviewed
  • [Journal Article] Spectral analysis and geometry of sub-Laplacian and related Grushin-type operators2011

    • Author(s)
      W. Bauer, K. Furutani, C. Iwasaki
    • Journal Title

      Oper. Thoery Adv. Appl.

      Volume: 211 Pages: 183-290

    • Peer Reviewed
  • [Journal Article] The Dirac-Hardy and Dirac-Sobolev inequalities in L^12011

    • Author(s)
      A. Balinsky, W. D. Evans, T. Umeda
    • Journal Title

      Publ. Res. Inst. Math. Sci.

      Volume: 47-3 Pages: 791-801

    • Peer Reviewed
  • [Journal Article] Eigenfunctions at the threshold energies of magnetic Dirac operators2011

    • Author(s)
      Y. Saito, T. Umeda
    • Journal Title

      Rev. Math. Phys

      Volume: 23-2 Pages: 155-178

    • Peer Reviewed
  • [Journal Article] A singular Cauchy problem For the Euler-Poisson-Darboux equation2010

    • Author(s)
      T. Watanabe
    • Journal Title

      J. Math. Pures. Appl.

      Volume: 93(9) Pages: 223-239

    • Peer Reviewed
  • [Journal Article] Construction of the fundamental solution and curvature of manifolds with boundary2009

    • Author(s)
      C. Iwassaki
    • Journal Title

      Oper. Thoery Adv. Appl.

      Volume: 189 Pages: 43-65

    • Peer Reviewed
  • [Journal Article] Semiclassical resonances for a two-level Schrodinger operator with a conical intersection2009

    • Author(s)
      S. Fujiie, C. Lasser, L. Nedel ec
    • Journal Title

      Asymptotic Analysis

      Volume: 65 1-2 Pages: 17-58

    • Peer Reviewed
  • [Presentation] Resonances created by homoclinic orbits associated with an isotropic equilibirum2011

    • Author(s)
      藤家雪朗
    • Organizer
      スペクトル・散乱理論とその周辺
    • Place of Presentation
      京都大学理学部(京都府)
    • Year and Date
      2011-12-15
  • [Presentation] Semiclassical resonances created by homoclinic orbits2011

    • Author(s)
      藤家雪朗
    • Organizer
      仙台シンポジウム
    • Place of Presentation
      東北大学情報理学研究科(宮城県)
    • Year and Date
      2011-08-25
  • [Presentation] Semi-classical width of resonances created by homoclinic orbits2011

    • Author(s)
      藤家雪朗
    • Organizer
      Scattering Theory-An International Workshop in Tokyo
    • Place of Presentation
      東京大学数理科学研究科(東京都)
    • Year and Date
      2011-06-22
  • [Presentation] Width of semiclassical resonances associated with homoclinic orbits2010

    • Author(s)
      藤家雪朗
    • Organizer
      Journees Mathematiques de Kairouan-E. D. P. et Applications
    • Place of Presentation
      Universite de Kairouen(チュニジア)
    • Year and Date
      2010-11-06
  • [Presentation] Resonance free domain for homoclinic trajectories2010

    • Author(s)
      藤家雪朗
    • Organizer
      The 8th Workshop on Linear and Nonlinear waves
    • Place of Presentation
      大阪大学理学部(大阪府)
    • Year and Date
      2010-09-10
  • [Presentation] Semiclassical resonances created by homoclinic orbits2010

    • Author(s)
      藤家雪朗
    • Organizer
      Recent Developments in Resurgence Theory and Related Topics
    • Place of Presentation
      関西セミナーハウス(京都府)
    • Year and Date
      2010-06-29

URL: 

Published: 2013-07-31  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi