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Analysis of superlattice structure using spectal analysis of Schroedinger operator

Research Project

Project/Area Number 20540204
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

OGURISU Osamu  金沢大学, 数物科学系, 准教授 (80301191)

Project Period (FY) 2008 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords超格子 / シュレーディンガー作用素 / 点相互作用 / スペクトル解析 / δポテンシャル / 負の固有値 / 離散ラプラシアン
Research Abstract

We studied spectral structure of some mathematical model of superlattice semiconductor device. Our results are as follows ; we studied the number of eigenvalues of Schroedinger operator with point interactions. In one dimensional case, we extended the known results under some restrictions to the ones without the restrictions. In two and three dimensional cases, though any results are unknown, we obtained the new results. We can treat discrete version of these models. We obtained similar results in one dimensional case and proved the dependence on the hyperbolicity in multidimensional cases.

Report

(6 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report   Self-evaluation Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (25 results)

All 2011 2010 2009 2008

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

  • [Journal Article] On the spectrum of a discrete Laplacian on Z with finitely supported potential2011

    • Author(s)
      Yuusuke Higuchi, Tomonori Matsumoto, Osamu Ogurisu
    • Journal Title

      Linear and Multilinear Algebra

      Volume: 59 Pages: 917-92

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the spectrum of a discrete Laplacian on (¥bf Z) with finitely supported potential2011

    • Author(s)
      Yu.HIGUCHI, T.MATSUMOTO, O.OGURISU
    • Journal Title

      Linear Multilinear Algebra

      Volume: 59 Issue: 8 Pages: 917-927

    • DOI

      10.1080/03081087.2010.536981

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Number of Negative Eigenvalues of a Schroedinger Operator withδInteractions2010

    • Author(s)
      Osamu Ogurisu
    • Journal Title

      Methods of Functional Analysis and Topology

      Volume: 16 Pages: 42-50

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Number of Negative Eigenvalues of a Multi-dimensional Schroedinger Operator with Point Interactions2010

    • Author(s)
      Osamu Ogurisu
    • Journal Title

      Methods of Functional Analysis and Topology

      Volume: 16 Pages: 383-392

    • Related Report
      2011 Final Research Report 2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Number of Negative Eigenvalues of a Multi-dimensional Schroedinger Operator with Point Interactions2010

    • Author(s)
      Osamu Oguirsu
    • Journal Title

      Methods of Functional Analysis and Topology 16

      Pages: 383-392

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the Number of Negative Eigenvalues of a Schroedinger Operator with δ Interactions2010

    • Author(s)
      Osamu Oguirsu
    • Journal Title

      Methods of Functional Analysis and Topology 16

      Pages: 42-50

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the Number of Negative Eigenvalues of a Schroedinger Operator with δ Interactions2010

    • Author(s)
      Osamu Oguirsu
    • Journal Title

      Methods of Functional Analysis and Topology

      Volume: 16 Pages: 42-50

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the number of negative eigenvalues of a Schrodinger operator with δ interactions2010

    • Author(s)
      Osamu Ogurisu
    • Journal Title

      Methods of Functional Analysis and Topology 16

      Pages: 42-50

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the Number of Negative Eigenvalues of a Schroedinger Operator with Point Interactions2008

    • Author(s)
      Osamu Ogurisu
    • Journal Title

      Letters in Mathematical Physics

      Volume: 85,(2-3) Pages: 1573-530

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Number of Negative Eigenvalues of a Schroedinger Operator with Point Interactions2008

    • Author(s)
      Osamu Oguirsu
    • Journal Title

      Letters in Mathematical Physics 85, (2-3)

      Pages: 1573-1530

    • Related Report
      2010 Self-evaluation Report
    • Peer Reviewed
  • [Journal Article] On the Number of Negative Eigenvalues of a Schroedinger Operator with Point Interactions2008

    • Author(s)
      Osamu Ogurisu
    • Journal Title

      Letters In Mathematical Physics 85

      Pages: 129-133

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Presentation] 有限個のポテンシャルを伴う離散ラプラシアンの固有値III2010

    • Author(s)
      小栗栖修,樋口雄介,野村祐司
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県)
    • Year and Date
      2010-12-15
    • Related Report
      2011 Final Research Report
  • [Presentation] 有限個のポテンシャルを伴う離散ラプラシアンの固有値 III2010

    • Author(s)
      小栗栖修, 樋口雄介, 野村祐司
    • Organizer
      応用数学合同研究集会1
    • Place of Presentation
      龍谷大学(滋賀県).
    • Year and Date
      2010-12-15
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 有限個のポテンシャルを伴う離散ラプラシアンの固有値III2010

    • Author(s)
      小栗栖修
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Year and Date
      2010-12-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] 有限個のポテンシャルを伴う離散ラプラシアンの固有値II2009

    • Author(s)
      小栗栖修,樋口雄介,松本知徳
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県)
    • Year and Date
      2009-12-16
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Presentation] 有限個のポテンシャルを伴う離散ラプラシアンの固有値 II2009

    • Author(s)
      小栗栖修, 樋口雄介, 松本知徳
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県).
    • Year and Date
      2009-12-16
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 影像インピーダンスを利用した変調超格子の準通過域情報の抽出2009

    • Author(s)
      浅倉邦彦
    • Organizer
      電子情報通信学会総合大会
    • Place of Presentation
      愛媛大学
    • Year and Date
      2009-03-18
    • Related Report
      2008 Annual Research Report
  • [Presentation] 散乱による電子波減衰を考慮した変調超格子の透過特性2009

    • Author(s)
      浅倉邦彦,小栗栖修,真田博文,鈴木正清
    • Organizer
      電子情報通信学会総合大会
    • Place of Presentation
      愛媛大学(愛媛県)
    • Year and Date
      2009-03-17
    • Related Report
      2011 Final Research Report
  • [Presentation] 散乱による電子波減衰を考慮した変調超格子の透過特性2009

    • Author(s)
      浅倉邦彦, 小栗栖修, 真田博文, 鈴木正清
    • Organizer
      電子情報通信学会総合大会
    • Place of Presentation
      愛媛大学.
    • Year and Date
      2009-03-17
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 回路理論の応用による変調超格子の準通過域情報の抽出2009

    • Author(s)
      浅倉邦彦,小栗栖修,真田博文,鈴木正清
    • Organizer
      電子情報通信学会回路とシステム研究会
    • Place of Presentation
      長良川国際会議場(岐阜県)
    • Year and Date
      2009-03-03
    • Related Report
      2011 Final Research Report
  • [Presentation] 回路理論の応用による変調超格子の準通過域情報の抽出2009

    • Author(s)
      浅倉邦彦, 小栗栖修, 真田博文, 鈴木正清
    • Organizer
      電子情報通信学会 回路とシステム研究会
    • Place of Presentation
      長良川国際会議場(岐阜県).
    • Year and Date
      2009-03-03
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 回路理論の応用による変調超格子の準通過域形成に関する-考察2009

    • Author(s)
      浅倉邦彦
    • Organizer
      電子情報通信学会
    • Place of Presentation
      岐阜県長良川国際会議場
    • Year and Date
      2009-03-02
    • Related Report
      2008 Annual Research Report
  • [Presentation] 有限個のポテンシャルを伴う離散ラプラシアンの固有値2008

    • Author(s)
      小栗栖修,樋口雄介,松本知徳
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県)
    • Year and Date
      2008-12-15
    • Related Report
      2011 Final Research Report
  • [Presentation] 有限個のポテンシャルを伴う離散ラプラシアンの固有値2008

    • Author(s)
      小栗栖修, 樋口雄介, 松本知徳
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県).
    • Year and Date
      2008-12-15
    • Related Report
      2010 Self-evaluation Report
  • [Presentation] 有限個のポテンシャルを伴う離散ラプラシアンの固有値2008

    • Author(s)
      小栗栖修
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      能谷大学
    • Year and Date
      2008-12-15
    • Related Report
      2008 Annual Research Report

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

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