Research on the problems of merging turning points via the semi-classical and microlocal analysis

• Project/Area Number: 22740094
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Ritsumeikan University
• Principal Investigator: WATANABE Takuya 立命館大学, 理工学部, 助教 (80458009)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 完全 WKB 解析 / 準古典解析 / 超局所解析 / 遷移確率 / 変わり点 / 完全WKB解析 / 断熱遷移確率（パリ） / 準古典超局所解析 / レゾナンス（ボローニャ） / 完全WKB法 / 断熱極限 / 擬交差 / 散乱行列

Research Abstract

In the two-level adiabatic transition probability with a small gap, we show how "turning points" and "Stokes lines", which are characterized by the so-called avoided crossings, affect the asymptotic behavior of the transition probability. The results gave us a great benefit for the future problems which include many turning points of higher degree.

Research Products

• [Journal Article] Characterization of PDE reducible to ODE under a certain homogeneity (2013)
  • Author(s): T . W at a na b e and J. Urabe
  • Journal Title: Funkcialaj Ekvacioj
  • Peer Reviewed
• [Journal Article] Singularities of solutions of the Fuchsian Cauchy problem with ramified data雑 誌 名 (2013)
  • Author(s): T . W at a na b e and J. Urabe
  • Journal Title: Journal of Mathematical Analysis and Applications
  • Peer Reviewed
• [Journal Article] Characterization of PDE reducible to ODE under a certain homogeneity (2013)
  • Author(s): T . Watanabe and J. Urabe
  • Journal Title: Funkcialaj Ekvacioj
  • Peer Reviewed
• [Journal Article] Characterization of PDE reducible to ODE under a certain homogeneity (2013)
  • Author(s): Takuya WATANABE and Jiichiroh URABE
  • Journal Title: Funkcialaj Ekvacioj Volume: 56
  • Peer Reviewed
• [Journal Article] Transition probability for multiple avoided crossings with a small gap through an exact WKB methodand a microlocal approach (2012)
  • Author(s): T . W atanabe and M.Zerzeri
  • Journal Title: Comptes Rendus de l'Academie des Sciences - Series I - Mathematics Volume: 350 Issue: 17-18 Pages: 841-844
  • DOI: 10.1016/j.crma.2012.10.005
  • Peer Reviewed
• [Journal Article] Exact WKB approach to 2-level adiabatic transition problems with a small spectral gap (2012)
  • Author(s): T . Watanabe
  • Journal Title: Tohoku MathematicalPublications Volume: 37 Pages: 1-80
  • URL: http://www.math.tohoku.ac.jp/tmj/TMP31to40.html
  • Peer Reviewed
• [Journal Article] Exact WKB approach to 2-level adiabatic transition problems with a small spectral gap (2012)
  • Author(s): Takuya WATANABE
  • Journal Title: Tohoku Mathematical Publications Volume: 37 Pages: 1-80
• [Journal Article] A singular Cauchy problem for the Euler-Poisson-Darboux equation (2010)
  • Author(s): T . Watanabe and J. Urabe
  • Journal Title: Journal de mathematiques pures et appliquees Volume: 93 / 3 Issue: 3 Pages: 223-239
  • DOI: 10.1016/j.matpur.2009.11.008
  • Peer Reviewed
• [Presentation] Transition probability for multiple avoided crossings with a small gap through an exact WKB method and a microlocal approach (2012)
  • Author(s): T. Watanabe
  • Organizer: Seminaires de l'equipe de Physique Mathematique et Equations aux Derivees Partielles 発表年月日
  • Place of Presentation: パリ(フランス)
  • Year and Date: 2012-12-03
• [Presentation] Asymptotic transition probability for multiple avoided crossings with a small gap (2012)
  • Author(s): 渡部 拓也
  • Organizer: 2012 夏の作用素論シンポジウ ム
  • Place of Presentation: 新潟大学(新潟県)
  • Year and Date: 2012-09-10
• [Presentation] Microlocal approach to two-level adiabatic transition probability for multiple avoided crossings with a small spectral gap(Part I, Part II) (2012)
  • Author(s): 渡部 拓也
  • Organizer: RIMS 共同研究「逆問題への応 用を意図した解析学の研究」
  • Place of Presentation: 京都数理解析研究所(京都府)
  • Year and Date: 2012-07-26
• [Presentation] Microlocal approach to two-level adiabatic transition probability for several avoided crossings with a small spectral gap (2012)
  • Author(s): T. Watanabe
  • Organizer: Seminari di Fisica Matematica, Universita di Bologna
  • Place of Presentation: ボローニャ(イタリア)
  • Year and Date: 2012-03-12
• [Presentation] Microlocal approach to two-level adiabatic transition probability for several avoided crossings with small spectral gap (joint work M.Zerzeri) (2012)
  • Author(s): Takuya WATANABE
  • Organizer: Seminari di Fisica Matematica
  • Place of Presentation: Universita di Bologna(イタリア)(招待講演)
  • Year and Date: 2012-03-12
• [Presentation] Microlocal approach to two-level adiabatic transition probability for several avoided crossings with a small spectral gap (2012)
  • Author(s): 渡部 拓也
  • Organizer: スペクトル散乱あきう(秋保) シンポジウム
  • Place of Presentation: 発表場所:ばんじ家(宮城県)
  • Year and Date: 2012-01-07
• [Presentation] Microlocal approach to two-level adiabatic transition probability for several avoided crossings with small spectral gap (joint work M.Zerzeri) (2012)
  • Author(s): Takuya WATANABE
  • Organizer: スペクトル・散乱あきうシンポジウム
  • Place of Presentation: 仙台市太白区秋保町ばんじ家(宮城県)
  • Year and Date: 2012-01-07
• [Presentation] Microlocal approach to two-level adiabatic transition probability for multiple avoided crossings with a small spectral gap (Part I, Part II) (2012)
  • Author(s): 渡部拓也
  • Organizer: RIMS共同研究「逆問題への応用を意図した解析学の研究」
  • Place of Presentation: 京都数理解析研究所 京都府
  • Invited
• [Presentation] Microlocal approach to two-level adiabatic transition probability for several avoided crossings with a small spectral gap (2011)
  • Author(s): 渡部 拓也 発
  • Organizer: 2011 年夏の作用素論シンポジ ウム
  • Place of Presentation: 熊本市国際交流会館(熊本県)
  • Year and Date: 2011-09-05
• [Presentation] Microlocal approach to two-level adiabatic transition probability for several avoided crossings with small spectral gap (joint work M.Zerzeri) (2011)
  • Author(s): Takuya WATANABE
  • Organizer: 2011年夏の作用素論シンポジウム
  • Place of Presentation: 熊本市国際交流会館(熊本県)
  • Year and Date: 2011-09-05
• [Presentation] Adiabatic transition probability for a small eigenvalue gap from the viewpoint of the exact WKB method (2011)
  • Author(s): T. Watanabe
  • Organizer: Seminaire: Problemes Spectraux en Physique Mathematique a l' Institut Henri Poincare 発
  • Place of Presentation: パリ(フランス)
  • Year and Date: 2011-03-07
• [Presentation] Adiabatic transition probability for a small eigenvalue gap from the viewpoint of the exact WKB method (2011)
  • Author(s): Takuya WATANABE
  • Organizer: Seminaire : Problemes Spectraux en Physique Mathematique
  • Place of Presentation: Institut Henri Poincare,パリ,フランス
  • Year and Date: 2011-03-07
• [Presentation] Connection problem between exact WKB solutions to $2times2$ system near simple turning points (2011)
  • Author(s): T. Watanabe
  • Organizer: Seminari di Fisica Matematica, Universita di Bologna
  • Place of Presentation: ボローニャ(イタリア)
  • Year and Date: 2011-02-28
• [Presentation] Connection problem between exact WKB solutions to $2times 2$ system near simple turning points (2011)
  • Author(s): Takuya WATANABE
  • Organizer: Seminari di Fisica Mathematica, Universita di Bologna
  • Place of Presentation: Bologna大学,ボローニャ,イタリア
  • Year and Date: 2011-02-28
• [Presentation] 同次性に基づいて常微分作用 素に帰着される偏微分作用素の特徴付 け (2011)
  • Author(s): 渡部 拓也
  • Organizer: 若手による偏微 分方程式における線形理論とその応用
  • Place of Presentation: 同志社大学(京都府)
  • Year and Date: 2011-01-13
• [Presentation] Adiabatic transition probability for a small eigenvalue gap from the viewpoint of the exact WKB method (2010)
  • Author(s): T. Watanabe
  • Organizer: Problemes spectraux en physique mathematique" d'Orsay
  • Place of Presentation: パリ(フランス)
  • Year and Date: 2010-12-15
• [Presentation] Adiabatic transition Probability for a small eigenvalue gap from the viewpoint of the exact WKB method (2010)
  • Author(s): Takuya WATANABE
  • Organizer: "Problemes spectraux en physique mathematique" d'Orsay
  • Place of Presentation: Paris 11大学,パリ,フランス
  • Year and Date: 2010-12-15
• [Presentation] ある同次性に基づいて常微分作用素に帰着される偏微分作用素の特 徴付け (2010)
  • Author(s): 渡部 拓也
  • Organizer: 第17回超局所解析と古典解 析研究集会
  • Place of Presentation: かんぽの宿 山代(石川県)
  • Year and Date: 2010-11-20
• [Presentation] フックス型特異初期値問題の 解の特異性 (2010)
  • Author(s): 渡部 拓也
  • Organizer: 日本数学会秋季総合分科会
  • Place of Presentation: 名古屋大学(愛知県)
  • Year and Date: 2010-09-22
• [Presentation] フックス型特異初期値問題の解の特異性 (2010)
  • Author(s): 渡部 拓也
  • Organizer: 2010夏の作用素論シンポジウム
  • Place of Presentation: 松本市中央公民館(長野県)
  • Year and Date: 2010-09-06
• [Presentation] Transition probability for multiple avoided crossings with a small gap through an exact WKB method and a microlocal approach
  • Author(s): Takuya WATANABE
  • Organizer: Se'minaires de l'e'quipe de Physique Mathe'matique et Equations aux De'rive'es Partielles
  • Place of Presentation: パリ フランス
  • Invited
• [Presentation] Asymptotic transition probability for multiple avoided crossings with a small gap
  • Author(s): 渡部拓也
  • Organizer: 2012年夏の作用素論シンポジウム
  • Place of Presentation: 新潟大学 新潟県
• [Presentation] Asymptotic transition probability for avoided crossings with a small gap (joint work with M.Zerzeri)
  • Author(s): 渡部拓也
  • Organizer: 東京理科大学 数学科談話会
  • Place of Presentation: 東京理科大学 千葉県
• [Presentation] Asymptotic transition probability for avoided crossings with a small gap (joint work with M.Zerzeri)
  • Author(s): 渡部拓也
  • Organizer: 大阪大学微分方程式セミナー
  • Place of Presentation: 大阪大学 大阪府
• [Remarks]
  • URL: http://www.math.ritsumei.ac.jp/takuwatanabe/lab/index.html
• [Remarks]
  • URL: http://research-db.ritsumei.ac.jp/Profiles/56/0005547/profile.html
• [Remarks]
  • URL: http://www.math.ritsumei.ac.jp/takuwatanabe/index.html
• [Remarks]
  • URL: http://research-db.ritsumei.ac.jp/Profiles/56/0005547/profile.html