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Analysis of superlattice structure using spectral analysis of non-linear Schroedinger operator

Research Project

Project/Area Number 24540208
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
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) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywordsスペクトル解析 / シュレーディンガー作用素 / 離散シュレーディンガー作用素 / 点相互作用 / 量子ウォーク / 関数方程式 / 数理物理 / スペクトル / 負の固有値 / 共鳴 / 離散グラフ / 離散ラプラシアン / δポテンシャル
Outline of Final Research Achievements

We studied spectral structure of some mathematical models of superlattice semiconductor devices. We studied the relation between the ratio of in-coming and out-going waves and the energy level E for perfect transmission, and found a kind of singularity. We also found that the relation between E and the phase factor, which is mentioned by RT effect, is broken. In another aspect, we introduced and studied the pseudo manifold of potentials for sustainability of resonances or embedded eigenvalues of discrete Schroedinger operator. In addition, we constructed quantum walks on simplicial complex as an application.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (13 results)

All 2016 2015 2014 2013 Other

All Journal Article (1 results) (of which Peer Reviewed: 1 results,  Open Access: 1 results,  Acknowledgement Compliant: 1 results) Presentation (11 results) (of which Int'l Joint Research: 1 results,  Invited: 4 results) Funded Workshop (1 results)

  • [Journal Article] Quantum walks on simplicial complexes2016

    • Author(s)
      Kaname Matsue, Osamu Ogurisu, Etsuo Segawa.
    • Journal Title

      Quantum Information Processing

      Volume: 15 Issue: 5 Pages: 1865-1896

    • DOI

      10.1007/s11128-016-1247-6

    • NAID

      120005743927

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Presentation] Quantum walks on simplicial complexes2015

    • Author(s)
      松江要、小栗栖修、瀬川悦生
    • Organizer
      Workshop of Quantum Simulation and Quantum Walks 2015
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2015-11-16
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 単体複体上の量子ウォークの構成2015

    • Author(s)
      瀬川悦生、小栗栖修、松江要
    • Organizer
      RIMS研究集会「量子場の数理とその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-10-05
    • Related Report
      2015 Annual Research Report
  • [Presentation] 単体的量子ウォーク:構築と問題定義2015

    • Author(s)
      松江要、小栗栖修、瀬川悦生
    • Organizer
      日本数学会秋季総合分科会応用数学分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Related Report
      2015 Annual Research Report
  • [Presentation] 離散シュレーディンガー作用素の埋め込まれた固有値について2015

    • Author(s)
      野村祐司、小栗栖修、樋口雄介
    • Organizer
      2015年夏の作用素論シンポジウム
    • Place of Presentation
      フェニックス・プラザ(福井市)
    • Year and Date
      2015-09-05
    • Related Report
      2015 Annual Research Report
  • [Presentation] 量子ウォーク - ダイナミクスと幾何構造 -2015

    • Author(s)
      松江要、小栗栖修、瀬川悦生
    • Organizer
      RIMS共同研究「デザイン、符号、グラフおよびその周辺」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-07-08
    • Related Report
      2015 Annual Research Report
  • [Presentation] 離散シュレーディンガー方程式の共鳴散乱と位相について2014

    • Author(s)
      小栗栖修
    • Organizer
      量子系の数理と物質制御への展開
    • Place of Presentation
      東北大学
    • Year and Date
      2014-09-17
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 点相互作用の負固有値の個数とその離散版について2014

    • Author(s)
      小栗栖修
    • Organizer
      多様体・格子・グラフ上のシュレーディンガー方程式のスペクトル・散乱理論
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-09-11 – 2014-09-12
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] グラフの局所最適性について2014

    • Author(s)
      小栗栖修
    • Organizer
      札幌数理物理研究集会
    • Place of Presentation
      北海道大学
    • Year and Date
      2014-09-01
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 点相互作用の負の固有値の個数と、その離散版について(仮)2014

    • Author(s)
      小栗栖修
    • Organizer
      多様体・格子・グラフ上のシュレディンガー方程式のスペクトル散乱理論
    • Place of Presentation
      数理解析研究所420号室
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 点相互作用の負固有値の個数2013

    • Author(s)
      小栗栖修
    • Organizer
      スペクトル・散乱松山シンポジウム
    • Place of Presentation
      愛媛大学愛大ミューズ
    • Related Report
      2012 Research-status Report
  • [Presentation] 有限個の点相互作用の離散版の研究

    • Author(s)
      小栗栖修
    • Organizer
      離散数学セミナー 2012 in 小山
    • Place of Presentation
      小山工業高等専門学校専攻科棟4階多目的メディアホール
    • Related Report
      2012 Research-status Report
  • [Funded Workshop] 2016 Symposium on Spectral and Scattering Theories in Kanazawa2016

    • Place of Presentation
      金沢大学サテライトプラザ(石川県金沢市)
    • Year and Date
      2016-01-09
    • Related Report
      2015 Annual Research Report

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Published: 2013-05-31   Modified: 2019-07-29  

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