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2022 Fiscal Year Research-status Report

量子流体力学に現れる確率偏微分方程式の研究

Research Project

Project/Area Number 19KK0066
Research InstitutionTohoku University

Principal Investigator

福泉 麗佳  東北大学, 情報科学研究科, 准教授 (00374182)

Co-Investigator(Kenkyū-buntansha) 星野 壮登  大阪大学, 大学院基礎工学研究科, 准教授 (20823206)
前田 昌也  千葉大学, 大学院理学研究院, 准教授 (40615001)
小林 未知数  高知工科大学, 環境理工学群, 准教授 (50433313)
戍亥 隆恭  大阪大学, 大学院理学研究科, 准教授 (70814648)
Project Period (FY) 2019-10-07 – 2024-03-31
Keywords量子流体 / 非線形シュレディンガー方程式 / 量子渦 / ボース・アインシュタイン凝縮
Outline of Annual Research Achievements

福泉は Deya, Thomann, 星野と共に非線形シュレディンガー方程式に加法的分数冪時空ノイズが加わったモデルについて, Hurst指数で表されるどの程度の正則性がノイズにあれば解の意味づけが出来るのかということについて研究を進めた. 前田は Refined profile の方法と virial の方法を融合することによりキンク解やソリトン解の局所漸近安定性について研究した. また,長距離ポテンシャルをもつ量子ウォークのスペクトル理論についても研究を行った.さらに,星野は Bailleulらと準線形一般化 KPZ 方程式の繰り込みを研究した.証明の確率論的な部分は宿題として残されているが,解析的な部分については,すべての劣臨界パラメータに対して繰り込み可能性を示すという,先行研究を大きく上回る結果を得た.小林は超伝導モデルで傑出した成果を出した. 超伝導では,非線形シュレディンガー方程式に電磁場を結合したモデルを考える必要があるが, 電磁場を結合することで量子渦間の相互作用は短距離力となり,電磁場と結合した量子渦の運動が超流動と比べて著しく変化することを考察した. 戌亥は, 1次元空間においてデルタ関数をポテンシャルに持つ非線形シュレディンガー方程式の解の大域ダイナミクスについて考察した. この方程式に対して, 解の対称性によってダイナミクスの閾値が変化し, またそれぞれの閾値上での解のダイナミクスも大きく異なることを示した.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

当初の研究計画に記述した以上の成果を多く出すことに成功している.

Strategy for Future Research Activity

国際共同研究を行ってはいるが, 新型コロナ感染症の影響で対面での議論を実現できていない. 今年度の成果をより発展させるために, 来年度は分担者全員に相手国での滞在を実現してもらい国際的な共同研究での成果をより多く出す予定である.

Causes of Carryover

コロナで出張が出来なかったため

  • Research Products

    (39 results)

All 2023 2022 Other

All Int'l Joint Research (4 results) Journal Article (16 results) (of which Int'l Joint Research: 9 results,  Peer Reviewed: 16 results,  Open Access: 3 results) Presentation (19 results) (of which Int'l Joint Research: 14 results,  Invited: 17 results)

  • [Int'l Joint Research] Universite de Lorraine/Univ. Rennes/Ecole Polytechnique(フランス)

    • Country Name
      FRANCE
    • Counterpart Institution
      Universite de Lorraine/Univ. Rennes/Ecole Polytechnique
    • # of Other Institutions
      3
  • [Int'l Joint Research] Universitat Stuttgart(ドイツ)

    • Country Name
      GERMANY
    • Counterpart Institution
      Universitat Stuttgart
  • [Int'l Joint Research] University of British Columbia(カナダ)

    • Country Name
      CANADA
    • Counterpart Institution
      University of British Columbia
  • [Int'l Joint Research] University of Trieste(イタリア)

    • Country Name
      ITALY
    • Counterpart Institution
      University of Trieste
  • [Journal Article] Small energy stabilization for 1D nonlinear Klein Gordon equations2023

    • Author(s)
      Cuccagna Scipio、Maeda Masaya、Scrobogna Stefano
    • Journal Title

      Journal of Differential Equations

      Volume: 350 Pages: 52~88

    • DOI

      10.1016/j.jde.2022.12.008

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Pattern Formation in 2D Stochastic Anisotropic Swift-Hohenberg Equation2023

    • Author(s)
      FUKUIZUMI Reika、GAO Yueyuan、SCHNEIDER Guido、TAKAHASHI Motomitsu
    • Journal Title

      Interdisciplinary Information Sciences

      Volume: 29 Pages: 81~98

    • DOI

      10.4036/iis.2023.a.03

    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Stationary martingale solution for the 2d stochastic Gross-Pitaevskii equation2023

    • Author(s)
      Anne de Bouard, Arnaud Debussche, Reika Fukuizumi
    • Journal Title

      RIMS講究録別冊

      Volume: / Pages: /

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Non relativistic and ultra relativistic limits in 2D stochastic nonlinear damped Klein-Gordon equation2022

    • Author(s)
      Fukuizumi Reika、Hoshino Masato、Inui Takahisa
    • Journal Title

      Nonlinearity

      Volume: 35 Pages: 2878~2919

    • DOI

      10.1088/1361-6544/ac64e0

    • Peer Reviewed
  • [Journal Article] Stochastic quantization associated with the exp (Phi)_2 -quantum field model driven by space-time white noise on the torus in the full L^1-regime2022

    • Author(s)
      Hoshino Masato、Kawabi Hiroshi、Kusuoka Seiichiro
    • Journal Title

      Probability Theory and Related Fields

      Volume: 185 Pages: 391~447

    • DOI

      10.1007/s00440-022-01126-z

    • Peer Reviewed
  • [Journal Article] Revisiting asymptotic stability of solitons of nonlinear Schroedinger equations via refined profile method2022

    • Author(s)
      Cuccagna Scipio、Maeda Masaya
    • Journal Title

      Journal of Evolution Equations

      Volume: 22 Pages: /

    • DOI

      10.1007/s00028-022-00806-6

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Asymptotic stability of small bound state of nonlinear quantum walks2022

    • Author(s)
      Maeda Masaya
    • Journal Title

      Physica D: Nonlinear Phenomena

      Volume: 439 Pages: 133408~133408

    • DOI

      10.1016/j.physd.2022.133408

    • Peer Reviewed
  • [Journal Article] On Selection of Standing Wave at Small Energy in the 1D Cubic Schroedinger Equation with a Trapping Potential2022

    • Author(s)
      Cuccagna Scipio、Maeda Masaya
    • Journal Title

      Communications in Mathematical Physics

      Volume: 396 Pages: 1135~1186

    • DOI

      10.1007/s00220-022-04487-7

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Asymptotic stability of kink with internal modes under odd perturbation2022

    • Author(s)
      Cuccagna Scipio、Maeda Masaya
    • Journal Title

      Nonlinear Differential Equations and Applications NoDEA

      Volume: 30 Pages: /

    • DOI

      10.1007/s00030-022-00806-y

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Core structures of vortices in Ginzburg-Landau theory for neutron 3P2 superfluids2022

    • Author(s)
      Kobayashi Michikazu、Nitta Muneto
    • Journal Title

      Physical Review C

      Volume: 105 Pages: /

    • DOI

      10.1103/PhysRevC.105.035807

    • Peer Reviewed
  • [Journal Article] Characterizing playing style with speed deviation2022

    • Author(s)
      Mai Takahashi, Michikazu Kobayashi, and Ikki Ohmukai
    • Journal Title

      Digital Humanities

      Volume: 2022 Pages: 692-695

    • Peer Reviewed / Open Access
  • [Journal Article] Non-delay limit in the energy space from the nonlinear damped wave equation to the nonlinear heat equation2022

    • Author(s)
      Inui Takahisa、Machihara Shuji
    • Journal Title

      Journal of Hyperbolic Differential Equations

      Volume: 19 Pages: 407~437

    • DOI

      10.1142/S0219891622500126

    • Peer Reviewed
  • [Journal Article] Asymptotic behavior for the long-range nonlinear Schroedinger equation on the star graph with the Kirchhoff boundary condition2022

    • Author(s)
      Aoki Kazuki、Inui Takahisa、Miyazaki Hayato、Mizutani Haruya、Uriya Kota
    • Journal Title

      Pure and Applied Analysis

      Volume: 4 Pages: 287~311

    • DOI

      10.2140/paa.2022.4.287

    • Peer Reviewed
  • [Journal Article] Threshold odd solutions to the nonlinear Schroedinger equation in one dimension2022

    • Author(s)
      Gustafson Stephen、Inui Takahisa
    • Journal Title

      Partial Differential Equations and Applications

      Volume: 3 Pages: /

    • DOI

      10.1007/s42985-022-00183-2

    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Interchanging Space and Time in Nonlinear Optics Modeling and Dispersion Management Models2022

    • Author(s)
      Fukuizumi Reika、Schneider Guido
    • Journal Title

      Journal of Nonlinear Science

      Volume: 32 Pages: /

    • DOI

      10.1007/s00332-022-09788-8

    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Two-Dimensional Gross-Pitaevskii Equation With Space-Time White Noise2022

    • Author(s)
      de Bouard Anne、Debussche Arnaud、Fukuizumi Reika
    • Journal Title

      International Mathematics Research Notices

      Volume: / Pages: /

    • DOI

      10.1093/imrn/rnac137

    • Peer Reviewed / Int'l Joint Research
  • [Presentation] Phase coexisting heat conduction in the Hamilton Potts model2023

    • Author(s)
      Michikazu Kobayashi
    • Organizer
      Japan-France joint seminar "Physics of dense and active disordred materials"
    • Int'l Joint Research / Invited
  • [Presentation] Machine-learning approach for detecting Kosterlitz-Thouless transition in the Gross-Pitaevskii and continuous clock models2023

    • Author(s)
      Michikazu Kobayashi
    • Organizer
      Mathematical Structures in Quantum Fluids
    • Int'l Joint Research / Invited
  • [Presentation] Smoluchowski-Kramers approximation in the stochastic nonlinear wave equation2023

    • Author(s)
      Reika Fukuizumi
    • Organizer
      RIMS 共同研究「Mathematical aspects of quantum fields and related topics」
    • Int'l Joint Research / Invited
  • [Presentation] Paracontrolled calculus and regularity structures2022

    • Author(s)
      Masato Hoshino
    • Organizer
      Deterministic Dynamics and Randomness in PDE
    • Int'l Joint Research / Invited
  • [Presentation] Paracontrolled calculus and regularity structures2022

    • Author(s)
      Masato Hoshino
    • Organizer
      Harmonic Analysis, Stochastics and PDEs in Honour of the 80th Birthday of Nicolai Krylov
    • Int'l Joint Research / Invited
  • [Presentation] A semigroup approach to the multi-level Schauder estimate2022

    • Author(s)
      Masato Hoshino
    • Organizer
      Probability and Analysis on Random Structures and Related Topics
    • Invited
  • [Presentation] A regularity structure for the quasilinear generalized KPZ equation2022

    • Author(s)
      Masato Hoshino
    • Organizer
      Geometry, Stochastics & Dynamics
    • Int'l Joint Research / Invited
  • [Presentation] Stochastic quantization associated with the exp(alpha phi)_2-quantum field model2022

    • Author(s)
      Masato Hoshino
    • Organizer
      Open Japanese-German conference on stochastic analysis and applications
    • Int'l Joint Research / Invited
  • [Presentation] A regularity structure for the quasilinear generalized KPZ equation2022

    • Author(s)
      Masato Hoshino
    • Organizer
      確率解析とその周辺
    • Int'l Joint Research / Invited
  • [Presentation] A regularity structure for the quasilinear generalized KPZ equation2022

    • Author(s)
      Masato Hoshino
    • Organizer
      確率論シンポジウム
  • [Presentation] Small energy stabilization of 1D Klein-Gordon equation with potential2022

    • Author(s)
      Masaya Maeda
    • Organizer
      第47回偏微分方程式論札幌シンポジウム
    • Int'l Joint Research / Invited
  • [Presentation] Violation of local equilibrium thermodynamics in phase coexistence under heat conduction2022

    • Author(s)
      Michikazu Kobayashi
    • Organizer
      Nonequilibrium Statistical Physics of Cooperative Systems
    • Int'l Joint Research / Invited
  • [Presentation] Time arrow in superfluid vortex dynamics2022

    • Author(s)
      Michikazu Kobayashi
    • Organizer
      6th Asia-Pacific Conference on Plasma Physics
    • Int'l Joint Research / Invited
  • [Presentation] Traveling waves for a nonlinear Schrodinger system with quadratic interaction2022

    • Author(s)
      林雅行, 戍亥隆恭, 深谷法良
    • Organizer
      日本数学会 2022 年度秋季総合分科会
  • [Presentation] デルタポテンシャル付き非線形シュレディンガー方程式の閾値解の大域ダイナミクスについて2022

    • Author(s)
      戍亥隆恭
    • Organizer
      第10回弘前非線形方程式研究会
    • Invited
  • [Presentation] Stochastic Gross-Pitaevskii equation2022

    • Author(s)
      Reika Fukuizumi
    • Organizer
      RIMS共同研究「Rigorous Statistical Mechanics and Related Topics」
    • Invited
  • [Presentation] Pattern formation in 2d stochastic anisotropic Swift-Hohenberg equation2022

    • Author(s)
      Reika Fukuizumi
    • Organizer
      RIMS共同研究「ランダム構造における確率論と解析学および関連する話題」
    • Int'l Joint Research / Invited
  • [Presentation] A stochastic effect in the quantum synchronization2022

    • Author(s)
      Reika Fukuizumi
    • Organizer
      Open Japanese-German conference on stochastic analysis
    • Int'l Joint Research / Invited
  • [Presentation] The stochastic logarithmic diffusion equation in R^d with a multiplicative Stratonovich noise2022

    • Author(s)
      Reika Fukuizumi
    • Organizer
      RIMS共同研究 「発展方程式論の革新:異分野との融合がもたらす 理論の深化」
    • Int'l Joint Research / Invited

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Published: 2023-12-25  

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