Updated on 2025/04/24

写真a

 
FUKUIZUMI, Reika
 
Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor
Degree
博士(理学) ( 2003.03 Tohoku University )
Mail Address
メールアドレス
Homepage URL
https://fukuizumi.w.waseda.jp

Research Experience

  • 2025.01
    -
    Now

    Osaka University   Graduate School of Engineering Science

  • 2023.04
    -
    Now

    Waseda University   Department of Mathematics, School of Fundamental Science and Engineering   Professor

  • 2022.07
    -
    Now

    理研革新知能統合(AIP) 研究センター客員研究員

  • 2024.09
    -
    2025.03

    フランス Ecole Polytechnique CMAP 招へい教授

  • 2022.04
    -
    2023.03

    東北大学   数理科学連携研究センター   構成員

  • 2008.10
    -
    2023.03

    東北大学情報科学研究科   准教授

  • 2022.09
    -
    2022.10

    フランス Universite de Rouen   招へい教授

  • 2017.04
    -
    2022.03

    東北大学数理科学連携研究センター   生命科学・社会数理構造解析研究部門構成員(兼務)

  • 2010.03
    -
    2010.06

    フランス, Ecole Polytechnique, CMAP(応用数学科)   Visiting Researcher

  • 2009.03
    -
    2009.06

    フランス, Ecole Polytechnique, CMAP(応用数学科)   Visiting Researcher

  • 2007.04
    -
    2008.09

    北海道大学理学研究院   数学専攻   助教

  • 2005.10
    -
    2007.09

    フランス, パリ第11大学   日本学術振興会海外特別研究員

  • 2004.04
    -
    2007.03

    北海道大学理学研究院   数学専攻   助手

  • 2003.04
    -
    2004.03

    東北大学理学研究科   数学専攻   日本学術振興会特別研究員PD

  • 2002.04
    -
    2003.03

    東北大学理学研究科   数学専攻   日本学術振興会特別研究員DC2

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Education Background

  • 2000.04
    -
    2003.03

    Tohoku University   Graduate School, Division of Natural Science   数学専攻  

  • 1998.04
    -
    2000.03

    The University of Tokyo   Graduate School, Division of Mathematical Sciences   数理科学専攻  

  • 1994.04
    -
    1998.03

    Waseda University   Faculty of Science and Engineering   数学科  

Committee Memberships

  • 2017.04
    -
    Now

    トリノ大学・トリノ工科大学（イタリア）応用・純粋数学科博士後期課程  外部審査委員

  • 2022.04
    -
    2023.03

    雑誌「数学通信」  常任編集委員

  • 2022.04
    -
    2023.03

    日本数学会東北支部  日本数学会東北支部連絡責任評議員

  • 2021.04
    -
    2023.03

    Journal of Interdisciplinary Information Sciences  編集委員

  • 2020.04
    -
    2021.03

    日本学術振興会  海外特別研究員審査員

  • 2019.04
    -
    2020.03

    ERC (European Research Council)  External reviewer for proposals in the evaluations of the ERC 2019 Starting, Consolidator, Advanced and Synergy Grant Calls

  • 2014.04
    -
    2015.03

    ANR (L’Agence Nationale de la Recherche)フランス科学研究費  外部審査員

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Professional Memberships

  • 　
    　
    　

    日本数学会

Research Areas

  • Basic analysis / Mathematical analysis / Mathematical physics and fundamental theory of condensed matter physics / Applied mathematics and statistics

Research Interests

  • Analysis

  • 非線形分散型方程式(超流動, 非線形光学, 量子グラフ)

  • (特異)確率偏微分方程式論(パターン形成, 同期現象, マルチスケール解析, 均質化)

  • 確率微分方程式の応用 (計算ファイナンス, 機械学習)

Awards

  • 第2回東北大学優秀女性研究者賞 紫千代萩賞

    2018   Tohoku University  

  • 2003年度東北大学大学院理学研究科黒田チカ賞

    2003   Tohoku University  

  • 建部賢弘奨励賞

    2003   日本数学会  

    Winner： 福泉 麗佳

 

Papers

  • The stochastic fast logarithmic equation in $\mathbb{R}^{d}$ with multiplicative Stratonovich noise

    Ioana Ciotir, Reika Fukuizumi, Dan Goreac

    Journal of Mathematical Analysis and Applications    2024  [Refereed]

  • Smoluchowski-Kramers approximation in the stochastic nonlinear damped wave equation in 2D

    Reika Fukuizumi

    数理解析研究所講究録 RIMS共同研究「量子場の数理とその周辺」    2023.10

  • On a critical fast diffusion stochastic equation with Stratonovich-type Brownian perturbation

    Ioana Ciotir, Reika Fukuizumi, Dan Goreac

    RIMS講究録「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」    2023.03

  • Pattern Formation in 2D Stochastic Anisotropic Swift–Hohenberg Equation

    Reika FUKUIZUMI, Yueyuan GAO, Guido SCHNEIDER, Motomitsu TAKAHASHI

    Interdisciplinary Information Sciences   29 ( 1 ) 81 - 98  2023.03  [Refereed]

    DOI

  • Corrigendum: Non relativistic and ultra relativistic limits in 2D stochastic nonlinear damped Klein–Gordon equation (2022 Nonlinearity 35 2878)

    Reika Fukuizumi, Masato Hoshino, Takahisa Inui

    Nonlinearity   35 ( 10 ) C17 - C19  2022.10  [Refereed]

    DOI

    Scopus

  • Non relativistic and ultra relativistic limits in 2D stochastic nonlinear damped Klein–Gordon equation

    Reika Fukuizumi, Masato Hoshino, Takahisa Inui

    Nonlinearity   35 ( 6 ) 2878 - 2919  2022.06  [Refereed]

    　View Summary

    Abstract

    We study the non relativistic and ultra relativistic limits in the two-dimensional nonlinear damped Klein–Gordon equation driven by a space-time white noise on the torus. In order to take the limits, it is crucial to clarify the parameter dependence in the estimates of solution. In this paper we present two methods to confirm this parameter dependence. One is the classical, simple energy method. Another is the method via Strichartz estimates.

    DOI

    Scopus

    3
    Citation
    (Scopus)

  • Interchanging Space and Time in Nonlinear Optics Modeling and Dispersion Management Models

    Reika Fukuizumi, Guido Schneider

    Journal of Nonlinear Science   32 ( 3 )  2022.06  [Refereed]

    　View Summary

    Abstract

    Interchanging the role of space and time is widely used in nonlinear optics for modeling the evolution of light pulses in glass fibers. A phenomenological model for the mathematical description of light pulses in glass fibers with a periodic structure in this set-up is the so-called dispersion management equation. It is the purpose of this paper to answer the question whether the dispersion management equation or other modulation equations are more than phenomenological models in this situation. Using Floquet theory we prove that in case of comparable wave lengths of the light and of the fiber periodicity the NLS equation and NLS like modulation equations with constant coefficients can be derived and justified through error estimates under the assumption that rather strong stability and non-resonance conditions hold. This is the first NLS approximation result documented for time-periodic dispersive systems. We explain that the failure of these conditions allows us to prove that these modulation equations in general make wrong predictions. The reasons for this failure and the behavior of the system for a fiber periodicity much larger than the wave length of light shows that interchanging the role of space and time for glass fibers with a periodic structure leads to unwanted phenomena.

    DOI

    Scopus

    1
    Citation
    (Scopus)

  • Two-Dimensional Gross–Pitaevskii Equation With Space-Time White Noise

    Anne de Bouard, Arnaud Debussche, Reika Fukuizumi

    International Mathematics Research Notices    2022.05  [Refereed]

    Authorship：Corresponding author

    　View Summary

    Abstract

    In this paper we consider the two-dimensional stochastic Gross–Pitaevskii equation, which is a model to describe Bose–Einstein condensation at positive temperature. The equation is a complex Ginzburg–Landau equation with a harmonic potential and an additive space-time white noise. We study the global well posedness of the model using an inhomogeneous Wick renormalization due to the potential and prove the existence of an invariant measure.

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • Stationary martingale solution for the 2d stochastic Gross-Pitaevskii equation

    Anne de Bouard, Arnaud Debussche, Reika Fukuizumi

    RIMS Bessatsu    2022  [Refereed]

    Authorship：Corresponding author

  • Stochastic Schrödinger-Lohe model

    Reika Fukuizumi, Leo Hahn

    Journal of Functional Analysis     109224 - 109224  2021.08  [Refereed]

    DOI

    Scopus

    2
    Citation
    (Scopus)

  • Scattering for the $L^2$ supercritical point NLS

    Riccardo Adami, Reika Fukuizumi, Justin Holmer

    Transactions of the American Mathematical Society   374 ( 1 ) 35 - 60  2020.10  [Refereed]

    DOI

    Scopus

    9
    Citation
    (Scopus)

  • Superfluidity and temperature effects

    R.Fukuizumi

       2020

  • A nonlinear quantum walk induced by a quantum graph with nonlinear delta potentials

    Riccardo Adami, Reika Fukuizumi, Etsuo Segawa

    Quantum information processing    2019  [Refereed]

  • Fluctuations and temperature effects in Bose-Einstein condensation

    Anne de Bouard, Arnaud Debussche, Reika Fukuizumi, Romain Poncet

    ESAIM: proceedings and surveys   61   55 - 67  2018.09  [Refereed]  [Invited]

  • Long time behavior of Gross-Pitaevskii equation at positive temperature

    Anne de Bouard, Arnaud Debussche, Reika Fukuizumi

    SIAM. J. Math. Anal.    2018  [Refereed]

  • Schrödinger equation with point nonlinearity

    Riccardo Adami, Reika Fukuizumi, Justin Holmer

    Oberwolfach Report    2017  [Invited]

  • Stationary problem related to the nonlinear Schrodinger equation on the unit ball (vol 25, pg 2271, 2012)

    Reika Fukuizumi, Fouad Hadj Selem, Hiroaki Kikuchi

    NONLINEARITY   28 ( 12 ) C3 - C7  2015.12  [Refereed]

    DOI

    Scopus

  • VORTEX SOLUTIONS IN BOSE-EINSTEIN CONDENSATION UNDER A TRAPPING POTENTIAL VARYING RANDOMLY IN TIME

    Anne de Bouard, Reika Fukuizumi, Romain Poncet

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B   20 ( 9 ) 2793 - 2817  2015.11  [Refereed]

    　View Summary

    The aim of this paper is to perform a theoretical and numerical study on the dynamics of vortices in Bose-Einstein condensation in the case where the trapping potential varies randomly in time. We take a deterministic vortex solution as an initial condition for the stochastically fluctuated Gross-Pitaevskii equation, and we observe the influence of the stochastic perturbation on the evolution. We theoretically prove that up to times of the order of epsilon(-2), the solution having the same symmetry properties as the vortex decomposes into the sum of a randomly modulated vortex solution and a small remainder, and we derive the equations for the modulation parameter. In addition, we show that the first order of the remainder, as epsilon goes to zero, converges to a Gaussian process. Finally, some numerical simulations on the dynamics of the vortex solution in the presence of noise are presented.

    DOI

    Scopus

  • Stationary States for Nonlinear Schrodinger Equations with Periodic Potentials

    Reika Fukuizumi, Andrea Sacchetti

    JOURNAL OF STATISTICAL PHYSICS   156 ( 4 ) 707 - 738  2014.08  [Refereed]

    　View Summary

    In this paper we consider a one-dimensional non-linear Schrodinger equation with a periodic potential. In the semiclassical limit we prove the existence of stationary solutions by means of the reduction of the non-linear Schrodinger equation to a discrete non-linear Schrodinger equation. In particular, in the limit of large nonlinearity strength the stationary solutions turn out to be localized on a single lattice site of the periodic potential. A connection of these results with the Mott insulator phase for Bose-Einstein condensates in a one-dimensional periodic lattice is also discussed.

    DOI

    Scopus

    9
    Citation
    (Scopus)

  • ランダムな外力を伴うグロス・ピタエフスキー方程式

    福泉麗佳

    数理解析研究所講究録 1823 RIMS 共同研究「偏微分方程式の背後にある確率過程と解の族が示す統計力学的な現象の解析」     158 - 171  2013

  • Representation formula for stochastic Schrodinger evolution equations and applications

    Anne de Bouard, Reika Fukuizumi

    NONLINEARITY   25 ( 11 ) 2993 - 3022  2012.11  [Refereed]

    　View Summary

    We prove a representation formula for solutions of Schrodinger equations with potentials multiplied by a temporal real-valued white noise in the Stratonovich sense. Using this formula, we obtain a dispersive estimate which allows us to study the Cauchy problem in L-2 or in the energy space of model equations arising in Bose-Einstein condensation, Abdullaev et al (2001 Nonlinearity and Disorder: Theory and Applications (NATO Science Series vol 45) ed F Abdullaev et al (Dodrecht: Kluwer)), or in fiber optics, Abdullaev et al (2000 Physica D 135 369-86). Our results also give a justification of diffusion-approximation for stochastic nonlinear Schrodinger equations.

    DOI

    Scopus

    15
    Citation
    (Scopus)

  • Stationary problem related to the nonlinear Schrodinger equation on the unit ball

    Reika Fukuizumi, Fouad Hadj Selem, Hiroaki Kikuchi

    NONLINEARITY   25 ( 8 ) 2271 - 2301  2012.08  [Refereed]

    　View Summary

    In this paper, we study the stability of standing waves for the nonlinear Schrodinger equation on the unit ball in R-N with Dirichlet boundary condition. We generalize the result of Fibich and Merle (2001 Physica D 155 132-58), which proves the orbital stability of the least-energy solution with the cubic power nonlinearity in two space dimension. We also obtain several results concerning the excited states in one space dimension. Specifically, we show the linear stability of the first three excited states and we give a proof of the orbital stability of the kth excited state, restricting ourselves to the perturbation of the same symmetry as the kth excited state. Finally, our numerical simulations on the stability of the kth excited state are presented.

    DOI

    Scopus

    13
    Citation
    (Scopus)

  • Bifurcation and Stability for Nonlinear Schrodinger Equations with Double Well Potential in the Semiclassical Limit

    Reika Fukuizumi, Andrea Sacchetti

    JOURNAL OF STATISTICAL PHYSICS   145 ( 6 ) 1546 - 1594  2011.12  [Refereed]

    　View Summary

    We consider the stationary solutions for a class of Schrodinger equations with a symmetric double-well potential and a nonlinear perturbation. Here, in the semiclassical limit we prove that the reduction to a finite-mode approximation give the stationary solutions, up to an exponentially small term, and that symmetry-breaking bifurcation occurs at a given value for the strength of the nonlinear term. The kind of bifurcation picture only depends on the nonlinearity power. We then discuss the stability/instability properties of each branch of the stationary solutions. Finally, we consider an explicit one-dimensional toy model where the double well potential is given by means of a couple of attractive Dirac's delta pointwise interactions.

    DOI

    Scopus

    18
    Citation
    (Scopus)

  • Modulation analysis for a stochastic NLS equation arising in Bose-Einstein condensation

    Anne de Bouard, Reika Fukuizumi

    ASYMPTOTIC ANALYSIS   63 ( 4 ) 189 - 235  2009.08  [Refereed]

    　View Summary

    We study the asymptotic behavior of the solution of a model equation for Bose-Einstein condensation, in the case where the trapping potential varies randomly in time. The model is the so called Gross-Pitaevskii equation, with a quadratic potential with white noise fluctuations in time whose amplitude E tends to zero. The initial condition of the solution is a standing wave solution of the unperturbed equation. We prove that up to times of the order of epsilon(-2), the solution decomposes into the sum of a randomly modulated standing wave and a small remainder, and we derive the equations for the modulation parameters. In addition, we show that the first order of the remainder, as c goes to zero, converges to a Gaussian process, whose expected mode amplitudes concentrate on the third eigenmode generated by the Hermite functions, on a certain time scale.

    DOI

    Scopus

    9
    Citation
    (Scopus)

  • Nonlinear Schrodinger equation with a point defect

    Reika Fukuizumi, Masahito Ohta, Tohru Ozawa

    ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE   25 ( 5 ) 837 - 845  2008.09  [Refereed]

    　View Summary

    We study the nonlinear Schrodinger equation with a delta-function impurity in one space dimension. Local well-posedness is verified for the Cauchy problem in H-1(R). In case of attractive delta-function, orbital stability and instability of the ground state is proved in H-1(R). (C) 2007 Elsevier Masson SAS. All fights reserved.

    DOI

    Scopus

    74
    Citation
    (Scopus)

  • Instability of bound states of a nonlinear Schrodinger equation with a Dirac potential

    Stefan Le Coz, Reika Fukuizumi, Gadi Fibich, Baruch Ksherim, Yonatan Sivan

    PHYSICA D-NONLINEAR PHENOMENA   237 ( 8 ) 1103 - 1128  2008.06  [Refereed]

    　View Summary

    We study analytically and numerically the stability of the standing waves for a nonlinear Schrodinger equation with a point defect and a power type nonlinearity. A major difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves. This is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing-wave solution is stable in H-rad(1)(R) and unstable in H-1(R) under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercritical nonlinear interaction, we prove the instability by blowup in the repulsive case by showing a virial theorem and using a minimization method involving two constraints. In the subcritical radial case, unstable bound states cannot collapse, but rather narrow down until they reach the stable regime (a finite-width instability). In the nonradial repulsive case, all bound states are unstable, and the instability is manifested by a lateral drift away from the defect, sometimes in combination with a finite-width instability or a blowup instability. (C) 2007 Elsevier B.V. All rights reserved.

    DOI

    Scopus

    77
    Citation
    (Scopus)

  • Stability of standing waves for a nonlinear Schrodinger equation with a repulsive Dirac delta potential

    Reika Fukuizumi, Louis Jeanjean

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   21 ( 1 ) 121 - 136  2008.05  [Refereed]  [Invited]

    　View Summary

    We consider a stationary nonlinear Schrodinger equation with a repulsive delta-function impurity in one space dimension. This equation admits a unique positive solution and this solution is even. We prove that it is a minimizer of the associated energy on the subspace of even functions of H-1(R, C), but not on all H-1(R, C), and study its orbital stability.

  • Stochastic fluctuations in the Gross-Pitaevskii equation

    Anne de Bouard, Reika Fukuizumi

    NONLINEARITY   20 ( 12 ) 2823 - 2844  2007.12  [Refereed]

    　View Summary

    We study from a mathematical point of view a model equation for a Bose-Einstein condensation, in the case where the trapping potential varies randomly in time. The model is the so-called Gross-Pitaevskii equation, with a quadratic potential with white noise fluctuations in time. We prove the existence of solutions in 1D and 2D in the energy space. The blow-up phenomenon is also discussed under critical and super critical nonlinear interactions in the attractive case.

    DOI

    Scopus

    3
    Citation
    (Scopus)

  • 非線形 Schrödinger 方程式の定在波解の安定性

    福泉麗佳

    数理解析研究所講究録1558「偏微分方程式に対する境界値問題」   65 ( 74 )  2007

  • On a decay property of solutions to the Haraux -Weissler equation,

    R. Fukuizumi, T. Ozawa

    Journal of Differential Equations.   221 ( no.1 ) 134 - 142  2006  [Refereed]

  • Stability of standing waves for nonlinear Schrodinger equations with inhomogeneous nonlinearities

    A De Bouard, R Fukuizumi

    ANNALES HENRI POINCARE   6 ( 6 ) 1157 - 1177  2005.12  [Refereed]

    　View Summary

    The effect of inhomogeneity of nonlinear medium is discussed concerning the stability of standing waves e(i omega t)phi(omega)(x) for a nonlinear Schrodinger equation with an inhomogeneous nonlinearity V (x)| u|(p-1)u, where V (x) is proportional to the electron density. Here, omega > 0 and phi(omega)(x) is a ground state of the stationary problem. When V ( x) behaves like | x|(-b) at infinity, where 0 < b < 2, we show that e(i omega t)phi(omega)(x) is stable for p < 1+(4-2b)/n and sufficiently small omega > 0. The main point of this paper is to analyze the linearized operator at standing wave solution for the case of V (x) = | x|(-b). Then, this analysis yields a stability result for the case of more general, inhomogeneous V (x) by a certain perturbation method.

    DOI

    Scopus

    49
    Citation
    (Scopus)

  • Exponential decay of solutions to nonlinear elliptic equations with potentials

    R Fukuizumi, T Ozawa

    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK   56 ( 6 ) 1000 - 1011  2005.11  [Refereed]

    　View Summary

    Exponential decay estimates are obtained for complex-valued solutions to nonlinear elliptic equations in R-n, where the linear term is given by Schrodinger operators H = -Delta + V with nonnegative potentials V and the nonlinear term is given by a single power with subcritical Sobolev exponent in the attractive case. We describe specific rates of decay in terms of V, some of which are shown to be optimal. Moreover, our estimates provide a unified understanding of two distinct cases in the available literature, namely, the vanishing potential case V = 0 and the harmonic potential case V (x) = |x|(2).

    DOI

    Scopus

    12
    Citation
    (Scopus)

  • STABILITY OF STANDING WAVES FOR NONLINEAR SCHRODINGER EQUATIONS WITH CRITICAL POWER NONLINEARITY AND POTENTIALS

    Reika Fukuizumi

    ADVANCES IN DIFFERENTIAL EQUATIONS   10 ( 3 ) 259 - 276  2005.03  [Refereed]

    　View Summary

    We study the stability of standing waves e(iwt)phi(omega)(x) for a nonlinear Schrodinger equation with critical power nonlinearity vertical bar u vertical bar(4/n)u and a potential V/(x) in R-n. Here, omega is an element of R and phi(omega)(x) is a ground state of the stationary problem. Under suitable assumptions on V(x), we show that e(iwt)phi(omega)(x) is stable for sufficiently large omega. This result gives a different phenomenon from the case V(x) equivalent to 0 where the strong instability was proved by M. I. Weinstein [25].

  • Instability of standing waves for nonlinear Schrodinger equations with inhomogeneous nonlinearities

    R Fukuizumi, N Ohta

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   45 ( 1 ) 145 - 158  2005  [Refereed]

  • Stability of standing waves for nonlinear Schrödinger equations with double power nonlinearity

    R. Fukuizumi

    数理解析研究所講究録1388「Nonlinear evolution equations and applications」   1388   23 - 33  2004

    CiNii

  • Stability of standing waves for nonlinear Schrödinger equations with potentials

    R. Fukuizumi

    Séminaire (2003-2004) Équations aux dérivées partielles, Ecole Polytechnique exposé numéro IX    2003

  • Remarks on the stable standing waves for nonlinear Schrödinger equations with double power nonlinearity,

    R. Fukuizumi

    Advances in Mathematical Sciences and Applications.   13 ( no.2 ) 549 - 564  2003  [Refereed]

  • Stability of standing waves for nonlinear Schrödinger equations with potentials,

    R. Fukuizumi, M. Ohta

    Differential and Integral Equations.   16 ( no.1 ) 111 - 128  2003  [Refereed]

  • Instability of standing waves for nonlinear Schrödinger equations with potentials,

    R. Fukuizumi, M. Ohta

    Differential and Integral Equations.   16 ( no.6 ) 691 - 706  2003  [Refereed]

  • Stability and instability of standing waves for nonlinear Schrödinger equations,

    R. Fukuizumi

    Tohoku Mathematical Publications   25  2003  [Refereed]

  • Stability and instability of standing waves for the nonlinear Schrodinger equation with harmonic potential

    R Fukuizumi

    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS   7 ( 3 ) 525 - 544  2001.07  [Refereed]

    　View Summary

    In this paper, we study the stability and the instability of standing waves for the nonlinear Schrodinger equation with harmonic potential. We prove the existence of stable or unstable standing waves under certain conditions on the power of nonlinearity and the frequency of wave.

  • Stability and instability of standing waves for nonlinear Schrödinger equations with harmonic potential

    R. Fukuizumi

    数理解析研究所講究録 1197「Nonlinear evolution equations and applications」   1197   196 - 206  2001

    CiNii

▼display all

Presentations

  • Explicit Bourgain Wick renormalization

    Reika Fukuizumi  [Invited]

    Presentation date： 2024.07

  • Modeling and analysis of superfluidity with a temperature effect

    Reika Fukuizumi  [Invited]

    International Workshop on Multiphase Flows: Analysis, Modelling and Numerics, Waseda University 

    Presentation date： 2023.12

    Event date：
    2023.12
    　
    　

  • Temperature effects in the BEC model

    Reika Fukuizumi  [Invited]

    Euro Japanese conference on Nonlinear Diffusion, ICMAT, Madrid 

    Presentation date： 2023.10

  • Random nonlinear Schrödinger equation

    Reika Fukuizumi  [Invited]

    Presentation date： 2023.10

  • A model of superfluidity with temperature effects

    Reika Fukuizumi  [Invited]

    Presentation date： 2023.09

    Event date：
    2023.09
    　
    　

  • Stochastically perturbed log diffusion equations

    Reika Fukuizumi  [Invited]

    ICIAM 2023 Tokyo, Nonlinear PDEs and related diffusion phenomena 

    Presentation date： 2023.08

  • Mathematical studies on the finite temperature BEC model

    Reika Fukuizumi  [Invited]

    Bridging Classical and Quantum Turbulence, QUTE-HPC workshop in Cargese, Corsica 

    Presentation date： 2023.07

    Event date：
    2023.07
    　
    　

  • Smoluchowski-Kramers approximation in the stochastic nonlinear wave equation

    Reika Fukuizumi  [Invited]

    2022 RIMS Mathematical aspects of quantum fields and related topics 

    Presentation date： 2023.01

  • Stochastic Gross-Pitaevskii equation

    福泉麗佳  [Invited]

    RIMS共同研究「Rigorous Statistical Mechanics and Related Topics」 

    Presentation date： 2022.11

  • Two dimensional Gross-Pitaevskii equation with space-time white noise

    福泉麗佳

    東北大・応用数理解析セミナー 

    Presentation date： 2022.10

  • The stochastic logarithmic diffusion equation in R^d with a multiplicative Stratonovich noise

    福泉麗佳  [Invited]

    RIMS共同研究（公開型） 「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」 

    Presentation date： 2022.10

  • A stochastic effect in the quantum synchronization

    R. Fukuizumi  [Invited]

    Open Japanese-German conference on stochastic analysis 

    Presentation date： 2022.09

  • Pattern formation in 2d stochastic anisotropic Swift-Hohenberg equation

    福泉麗佳  [Invited]

    RIMS共同研究（公開型）「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」 

    Presentation date： 2022.08

  • A nonlinear Kronig-Penney model

     [Invited]

    Presentation date： 2022.05

  • Statistical thermodynamics in the BEC model

     [Invited]

    Presentation date： 2022.03

    Event date：
    2022.03
    -
    　

  • 有限温度のボース・アインシュタイン凝縮を記述する確率微分方程式

    R.Fukuizumi

    東京工業大学量子物理学・ナノサイエンスセミナー第323回セミナー 

    Presentation date： 2021.10

  • Nonlinear Schrodinger equation: soliton, blow-up and noise

    Presentation date： 2021.09

  • Stochastic models arising in quantum phenomena

    R. Fukuizumi

    Presentation date： 2021.07

    Event date：
    2021.07
    　
    　

  • Superfluidity and temperature effects

    R. Fukuizumi

    京都大学数理解析研究所RIMS共同研究(公開型) 量子場の数理とその周辺 

    Presentation date： 2021.03

    Event date：
    2021.03
    　
    　

  • Gibbs Equilibrium for Gross-Pitaevskii equation

    R. Fukuizumi

    Quantum and Kinetic Problems: Modeling, Analysis, Numerics and Applications, Workshop 1: Recent Progress and Challenge in Quantum and Kinetic Problems, National University of Singapore, Singapore 

    Presentation date： 2019

    Event date：
    2019.09
    -
    2019.10

  • Gibbs Equilibrium for Gross-Pitaevskii equation

    R. Fukuizumi  [Invited]

    Lorraine-Tohoku Workshop, Université de Lorraine, Nancy, France 

    Presentation date： 2019

    Event date：
    2019.09
    　
    　

  • Temperature effects and longtime behaviour of Gross-Pitaevskii equation

    R. Fukuizumi

    Colloquium at Universität Stuttgart, Stuttgart, Germany 

    Presentation date： 2019.09

  • Stochastic damped nonlinear wave equation: a model of finite temperature superconductivity

     [Invited]

    Workshop on nonlinear PDE in Numazu 

    Presentation date： 2019.06

  • BEC model with a trapping potential varying randomly in time- a review

    R. Fukuizumi  [Invited]

    Scientific Computing Across Scales: Quantum Systems in Cold-matter Physics and Chemistry, Fields Institute, Toronto, Canada 

    Presentation date： 2019.04

  • On the stochastic Gross-Pitaevskii equation

     [Invited]

    Okayama Workshop on Stochastic Analysis 2019, 岡山大学 

    Presentation date： 2019.02

  • Recent progress of theoretical and numerical research for BEC models

    R. Fukuizumi

    研究会「第４回量子渦と非線形波動」東京理科大学 

    Presentation date： 2019.01

  • Bose-Einstein 凝縮モデルにおける温度効果

    R. Fukuizumi  [Invited]

    「日本数学会 2018 年度秋季総合分科会特別講演」 岡山大学 

    Presentation date： 2018.09

  • Scattering in the Schrödinger equation with a point nonlinearity

    R. Fukuizumi  [Invited]

    The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taipei, Taiwan 

    Presentation date： 2018.07

  • Some theoretical studies on the stochastic Gross-Pitaevskii equation

    R. Fukuizumi  [Invited]

    The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taipei, Taiwan 

    Presentation date： 2018.07

  • On the stochastic Gross-Pitaevskii equation

    R. Fukuizumi  [Invited]

    Conference of Mathematics on Wave Phenomena, KIT, Germany 

    Presentation date： 2018.07

  • Recent progress of theoretical and numerical research for BEC models

    R.Fukuizumi  [Invited]

    研究会「第４回量子渦と非線形波動」東京理科大学 

    Presentation date： 2018.01

  • On the Gibbs equilibrium in stochastic complex Ginzburg-Landau Equations

    R. Fukuizumi

    「2017年確率論シンポジウム」東北大学片平キャンパスさくらホール 

    Presentation date： 2017.12

  • A singular complex Ginzburg-Landau equation: Global existence and Gibbs measure

    Presentation date： 2017.12

  • 量子流体の数理モデル

    R.Fukuizumi

    東北大学情報科学研究科棟 談話会「第72回情報科学談話会」 

    Presentation date： 2017.11

  • Gross-Pitaevskii equation at positive temperature

    R. Fukuizumi  [Invited]

    「LMRS Colloquium」 ルーアン大学, フランス 

    Presentation date： 2017.10

  • Schrödinger equation with point nonlinearity

    R. Fukuizumi

    Workshop「Nonlinear Partial Differential Equations on Graphs」Oberwolbach数学研究所, ドイツ 

    Presentation date： 2017.06

  • Long time behaviour of Gross-Pitaevskii equation at positive temperature

    R. Fukuizumi  [Invited]

    「第18回北東数学研究集会」東北大学 

    Presentation date： 2017.02

  • Exponential convergence to the equilibrium for the stochastic Ginzburg-Landau equation

    R. Fukuizumi  [Invited]

    研究会「第３回量子渦と非線形波動」東京理科大学 

    Presentation date： 2016.11

  • Exponential convergence to the equilibrium for the stochastic Gross-Pitaevskii equation

    R. Fukuizumi  [Invited]

    IMA 研究集会「Mathematical and Physical Models of Nonlinear Optics」ミネソタ大学, アメリカ合衆国 

    Presentation date： 2016.10

  • Gibbs measure for the Gross-Pitaevskii equation driven by a space-time white noise

    R. Fukuizumi  [Invited]

    研究会「量子渦と非線形波動」東京理科大学 

    Presentation date： 2016.01

  • Stochastic GP 方程式における渦解

    R. Fukuizumi  [Invited]

    研究会「量子渦と非線形波動」東京理科大学 

    Presentation date： 2015.01

  • Vortex solutions in Bose-Einstein Condensation

    R. Fukuizumi

    研究集会「確率解析とその周辺」東北大学 

    Presentation date： 2014.10

  • Vortex solutions in BEC under a trapping potential varying randomly in time

    R. Fukuizumi  [Invited]

    Politecnico di Torino, イタリア 

    Presentation date： 2014.10

  • 非線形Schrödinger 方程式-定在波とノイズ

    R.Fukuizumi  [Invited]

    RIMS共同研究「偏微分方程式に付随する確率論的問題」京都大学数理解析研究所 

    Presentation date： 2014.09

  • Gross-Pitaevskii equation with noise

    R. Fukuizumi  [Invited]

    研究集会「Analytical and Numerical Advances around Schrödinger equations」Toulouse 第３大学, フランス 

    Presentation date： 2012.10

  • Derivation of Bose-Hubbard model-Approximation by DNLS

    R.Fukuizumi  [Invited]

    研究集会「光ファイバーとそれに関連する非線形偏微分方程式の研究」九州大学マス・フォア・インダストリ研究所 

    Presentation date： 2012.08

  • ノイズが定在波に与える影響について

    R.Fukuizumi  [Invited]

    OCAMI楕円型方程式研究集会 大阪市立大学 

    Presentation date： 2011.08

  • Bifurcation and stability of semiclassical bound states of NLS with two point interactions

    R. Fukuizumi  [Invited]

    「第28 回九州における偏微分方程式研究集会」 九州大学 

    Presentation date： 2011.01

  • A limit Theorem in stochastic nonlinear Schrodinger equations

     [Invited]

    Presentation date： 2010.12

  • Stochastic fluctuations in the Gross-Pitaevskii equation

    R. Fukuizumi

    研究集会「Model equations in Bose-Einstein Condensation and related topics」 京都大学 

    Presentation date： 2010.12

  • Estimation dispersive pour des équations de Schrödinger avec un potentiel stochastique

    R. Fukuizumi  [Invited]

    Ecole Polytechnique, フランス 

    Presentation date： 2010.11

  • Diffusion approximation for a stochastic GP equation

    R.Fukuizumi  [Invited]

    Workshop on solitary waves and related topics 九州大学 

    Presentation date： 2010.07

  • Stability analysis of bound states for NLS before and after a symmetry breaking in the semiclassical regime

     [Invited]

    Hiroshima Mathematical Analysis Seminar No.140 

    Presentation date： 2010.07

  • Representation formula for stochastic Schrödinger equations

    R. Fukuizumi  [Invited]

    研究集会「Nonlinear Schrödinger Equations」Modena e Reggio Emilia大学, イタリア 

    Presentation date： 2010.06

  • Estimation dispersive pour des équations de Schrödinger avec un potentiel stochastique

    R. Fukuizumi  [Invited]

    Montpellier 第２大学, フランス 

    Presentation date： 2010.06

  • Dynamics of solitons for a stochastic nonlinear Schrödinger equation

    R. Fukuizumi  [Invited]

    RIMS 研究集会「孤立波の安定性と変分問題」埼玉大学 

    Presentation date： 2010.01

  • Modulation analysis for a stochastic NLS arising in Bose-Einstein Condensation

    R. Fukuizumi  [Invited]

    研究集会「Stochastic problems and nonlinear PDEs」京都大学 

    Presentation date： 2008.12

  • On drift instability of bound states of nonlinear Schrodinger equations

     [Invited]

    Presentation date： 2008.06

  • Stochastic fluctuations in the Gross-Pitaevskii equation

    R. Fukuizumi  [Invited]

    「Stochastic Problems and Nonlinear PDEs」京都大学 

    Presentation date： 2007.12

  • A stochastic NLS equation arising in Bose-Einstein condensation

    R. Fukuizumi  [Invited]

    「確率論とPDE」広島大学 

    Presentation date： 2007.10

  • Nonlinear Schrödinger equation with a point defect

    R. Fukuizumi

    「Nonlinear evolution equation and wave phenomena: computation and theory」 Athens, Georgia,アメリカ合衆国 

    Presentation date： 2007.04

  • Equation de Schrödinger non linéaire avec un defaut localisé

    R. Fukuizumi

    GDR MOAD, Lille 第一大学,フランス 

    Presentation date： 2007.03

  • Stability of standing waves for a nonlinear Schrodinger equation with a repulsive Dirac delta potential

    R. Fukuizumi  [Invited]

    Wolfgang Pauli Institute, 「Modern Applications of Gross-Pitaevskii equations: The Bose-Einstein Condensation」Vienna,オーストリア 

    Presentation date： 2006.11

  • 非線型Schrödinger方程式の定在波解の安定性

    R. Fukuizumi  [Invited]

    「非線形偏微分方程式に対する境界値問題」京都大学数理解析研究所 

    Presentation date： 2005.05

  • On the standing wave solutions for some nonlinear Schrödinger equations

     [Invited]

    「微分方程式の総合的研究」東京大学 

    Presentation date： 2004.12

  • Weighted estimates of the solutions to some semi linear elliptic equations

    R. Fukuizumi  [Invited]

    「Stochastic Problems and Nonlinear PDEs」京都大学 

    Presentation date： 2004.11

  • Convergence property of variation problems related to nonlinear Schrödinger equations and its applications

    R. Fukuizumi

    「第7回ソウル大-北大ジョイントシンポジウム」北海道大学 

    Presentation date： 2004.07

  • Stability of standing waves for the nonlinear Schrödinger equations with critical power nonlinearity and harmonic potential

    R.Fukuizumi

    日本数学会2003年度年会 千葉大学 

    Presentation date： 2003.09

  • Instability of standing waves for nonlinear Schrödinger equations with inhomogeneous nonlinearities

    R.Fukuizumi

    日本数学会2003年度年会 千葉大学 

    Presentation date： 2003.09

  • Instability of standing waves for nonlinear Schr\"odinger equations in nonhomogeneous media

     [Invited]

    Presentation date： 2003.03

  • Instability of standing waves for nonlinear Schrödinger equations in nonhomogeneous media

    R. Fukuizumi  [Invited]

    「Nonlinear Wave Equations and Related Fields」名古屋大学 

    Presentation date： 2003.02

  • Convergence property of variational problems related to nonlinear Schrödinger equations and its applications

    R.Fukuizumi  [Invited]

    第4回北東数学解析研究集会 東北大学 

    Presentation date： 2003.02

  • Stability and instability of standing waves for the nonlinear Schrödinger equations with harmonic potential

    R. Fukuizumi  [Invited]

    「研究集会：非線形波動及び消散型方程式の解の性質について」大阪大学 

    Presentation date： 2002.11

  • Convergence property of variational problems related to nonlinear Schrödinger equations and its applications

    R. Fukuizumi  [Invited]

    研究集会：非線形波動及び消散型方程式の解の性質について」大阪大学 

    Presentation date： 2002.10

  • Stability of standing waves for the nonlinear Schrödinger equations with double power nonlinearity

    R. Fukuizumi  [Invited]

    「調和解析学と非線形偏微分方程式」京都大学数理解析研究所 

    Presentation date： 2002.07

  • Stability of standing waves for the nonlinear Schrödinger equations with double power nonlinearity in higher dimensions

    R.Fukuizumi

    日本数学会2002年度年会 関数方程式分科会 明治大学 

    Presentation date： 2002.03

  • Stability of standing waves for the nonlinear Schrödinger equations with double power nonlinearity

    R.Fukuizumi  [Invited]

    第３回北東数学解析研究集会 札幌天神山国際ゲストハウス 

    Presentation date： 2002.02

  • Stability of standing waves for the nonlinear Schrödinger equations with unbounded potentials

    R.Fukuizumi

    日本数学会 関数方程式論分科会 九州大学 

    Presentation date： 2001.10

  • Stability of standing waves for the nonlinear Schrödinger equations with potentials

    R. Fukuizumi  [Invited]

    「第26回偏微分方程式論札幌シンポジウム」 北海道大学 

    Presentation date： 2001.07

  • Instability of stationary states for nonlinear Schrödinger equations with magnetic field

    R.Fukuizumi

    日本数学会 20001年度年会 関数方程式論分科会 慶応大学 

    Presentation date： 2001.03

  • Stability of standing waves for the nonlinear Schrödinger equations with unbounded potentials

    R.Fukuizumi  [Invited]

    第2回北東数学解析研究集会 東北大学 

    Presentation date： 2001.02

  • Stability and instability of standing waves for the nonlinear Schrödinger equations with harmonic potential

    R. Fukuizumi  [Invited]

    京都大学数理解析研究所 

    Presentation date： 2000.10

  • Instability of standing waves for nonlinear Schrödinger equations with potentials

    R.Fukuizumi

    日本数学会2002年度年会 関数方程式分科会 京都大学 

    Presentation date： 2000.09

  • Stability of standing waves for the nonlinear Schrödinger equations with harmonic potential

    R.Fukuizumi

    日本数学会 2000年度年会 関数方程式論分科会 早稲田大学 

    Presentation date： 2000.03

  • Stability of standing waves for the nonlinear Schrödinger equations with harmonic potentials

    R.Fukuizumi  [Invited]

    第１回北東数学研究集会 札幌天神山国際ゲストハウス 

    Presentation date： 2000.02

▼display all

Research Projects

  • 非線形分散型及び波動方程式における特異なランダム動力学

    日本学術振興会  科学研究費助成事業

    Project Year :

    2023.04
    -
    2027.03
     

    福泉 麗佳, 星野 壮登, 前田 昌也, 岡本 葵

  • Macroscopic properties of discrete stochastic models and analysis of their scaling limits

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2023.09
    -
    2026.03
     

  • Mathematical and Physical Models for Superfluids and Superconductors

    CNRS  CNRS International Emerging Actions

    Project Year :

    2022.01
    -
    2023.12
     

    Ionut Danaila, Takashi Sakajo, Reika Fukuizumi, Michikazu Kobayashi, Marc-Etienne Brachet, Jean-Guy Caputo, Luminita Danaila

  • 非線形シュレディンガー方程式における確率的効果

    日本学術振興会  科学研究費助成事業 基盤研究(C)

    Project Year :

    2020.04
    -
    2023.03
     

    福泉 麗佳

    　View Summary

    電磁波を記述する基礎方程式はMaxwell方程式であるが, 光ファイバー中を伝播する光波のモデリングは, Maxwell方程式に非線形媒質効果を取り入れて近似をした後で波の包絡線の時間発展の方程式として導出される非線形 Schrodinger方程式で行われる. 一方, 分散マネージメント光ファイバーという昔から実際に導入されてきた光ファイバー技術がある. その技術とは, 入力した波が元来持つ分散性によりエネルギー損失が起こるのを防ぐために, 分散性をランダムにあるいは周期的に符号変化させて分散の平均をゼロとするようなファイバーを作るというものである. しかしながら, この分散マネージメント光ファイバーのモデル方程式はランダムあるいは周期的な係数を考慮したMaxwell方程式の近似として非線形Schrodinger方程式で表現されるものなのか, しかも分散マネージメント効果というのは導出した非線形Schrodinger方程式のどこに現れてくるのかという疑問が以前から問われていた. この問いに対して, 否定的な解答（例）を得, 単独の非線形 Schrodinger方程式でなく, 非線形Schrodingerのシステムが近似であるはずだという結論を導いた. Lohe (2010 J. Phys. A.)が発表した論文中には「量子同期モデル」と呼ばれる Kuramotoモデルの量子版で非線形シュレディンガー方程式を用いたモデルが提案されている. Loheの提唱モデルは量子デバイス中に量子同期を起こすことにより, 情報をより安定して送ることができるのではないかという発想からきている. そこで2014年あたりから同期の数学的定義に始まり, 時間が十分経った後, どのような種類の同期を起こしているのか等を多くの数学者たちが研究を盛んに行ってきた. しかし, 同期現象がノイズの影響を受けてどのような変化をするかという問いは完全に未解決であった. このノイズの影響を L. Hahn 氏と共に研究した.

  • 量子流体力学に現れる確率偏微分方程式の研究

    日本学術振興会  科学研究費助成事業 国際共同研究加速基金(国際共同研究強化(B))

    Project Year :

    2019.10
    -
    2023.03
     

    福泉 麗佳, 星野 壮登, 前田 昌也, 小林 未知数, 戍亥 隆恭

    　View Summary

    研究代表者は、3月にフランスへ出張し、Universite de Rouen において講演を行い Ionut Danaila が率いる量子乱流数値実験グループと共同研究の確認を行う予定であったが、新型コロナウイルスの影響で中止となった。研究代表者は同じ時期に Paris にも立ち寄り Ecole Polytechnique において Anne de Bouard と温度効果を考慮した Bose-Einstein 凝縮モデルの長時間挙動について議論を行う予定であったが、これも新型コロナウイルスの影響で遂行ができなかった。 研究分担者星野もフランスへ出張する予定があったが新型コロナウイルスの影響を鑑みて中止とした。 このような状況であるが、 昨年度、 研究代表者は de Bouard, Debussche と温度効果を伴う Bose-Einstein 凝縮モデルにおいて、 空間2次元で Gibbs 不変測度を構成し、それを利用して大域解の存在を示すことに成功し現在論文を執筆中である。 また、研究分担者である小林は、 Danaila らと共同研究を実施し、 量子乱流を数値的に扱う複数のアルゴリズムおよび Gross-Pitaevskii方程式を高速で解くための複数のアルゴリズムを議論した。 様々な状況下における量子乱流シミューションの数値計算効率を比較し、成果をまとめた論文「Quantum turbulence simulations using the Gross-Pitaevskii equation: high-performance computing and new numerical benchmarks」が査読中の段階にある。

  • Nonlinear and Random Waves

    Project Year :

    2022.04
    -
    2023.03
     

    Reika Fukuizumi, Anne de Bouard

  • 量子流体における数理構造の解明

    大阪公立大学数学研究所  大阪公立大学数学研究所共同研究(B)

    Project Year :

    2022.04
    -
    2023.03
     

    福泉麗佳, 小林未知数, 坂上貴之, 坪田誠

  • Geometry of partial differential equations and inverse problems

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2018.04
    -
    2022.03
     

  • 共同研究(B): 量子渦と非線形波動

    文部科学省  文部科学省共同利用・共同研究拠点「数学・理論物理の協働・共創による新たな国際的研究・教育拠点」

    Project Year :

    2019.04
    -
    2020.03
     

    小林未知数

  • 量子流体力学に応用される確率偏微分方程式の研究

    東北大学数理連携研究センター  2019年度 東北大学数理連携研究センター研究費

    Project Year :

    2019.04
    -
    2020.03
     

  • Analysis of quantum turbulence by stochastic PDEs

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Project Year :

    2016.07
    -
    2019.03
     

    Fukuizumi Reika, Anne de Bouard, Poncet Romain, Debussche Arnaud

    　View Summary

    We proved in one dimension the existence of unique global solution of Gross-Pitaevskii equation at positive temperature (i.e. nonlinear Schroedinger equation with a dissipation and space-time white noise), and showed that the law of solution converges exponentially to the Gibbs equilibrium as time goes to infinity. In the proof of the globalization of solution, we succeeded to make a globalization for any initial data by the Strong Feller property of transition semigroup. Also, we verified the similar facts in two dimensional case.

  • Research of nonlinear dispersive equations with stochastic effects

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)

    Project Year :

    2015.04
    -
    2019.03
     

    Fukuizumi Reika, Adami Riccardo, Holmer Justin, Segawa Etsuo, Anne de Bouard, Poncet Romain, Debussche Arnaud

    　View Summary

    We studied a model that describes a wave propagation in a one-dimensional linear medium containing a narrow strip of nonlinear material, where the nonlinear strip is assumed to be much smaller than the typical wavelength. This model is used, for example, a wave propagation in nanodevices. We showed that for a large non linearity (called mass super critical), if the initial energy is below the energy of the ground state, the solution scatters in the energy class. Moreover we investigated the asymptotic distribution of the quantum walk associated with this nanodevice model.
    On the other hand, we considered the Gross-Pitaevskii equation at positive temperature, where the temperature effect is described by a dissipation and white noise in the equation. We showed that the system converges exponentially to the Gibbs equilibrium as times goes to infinity, in one spatial dimension.

  • Study on structural analysis of networks by quantum walks

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Project Year :

    2013.04
    -
    2016.03
     

    Etsuo Segawa, Konno Norio, Sato Iwao, Higuchi Yusuke, Fukuizumi Reika, Adami Riccardo

    　View Summary

    In this research, we studied a mathematical model named quantum walk, which is investigated as quantum speed up quantum search algorithm and also a nice model accomplishing a topological insulator. In particular, by many time iterations of quantum walks on a network, we attempted to extract some structures of the network. By measuring a quantum walk on infinite graph after sufficiently large time, then we can know the existence of cycles and edges of the network as localization phenomena. We also observe its opposite property named linear spreading simultaneously. This phenomena provides which takes a quantum walker to quadratically further place comparing with random walker with respect to time iterations.

  • Stochastic Processes and Statistical Phenomena behind Partial Differential Equaitons

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2011.04
    -
    2016.03
     

    NAWA Hayato, SAKAJO Takashi, YOSHIDA Nobuo, FUKUIZUMI Reika, Matsumoto Takeshi, AKAHORI Takafumi, KIKUCHI Hiroaki, Gadi Fibich, Anne de Bouard, OHKITANI Koji

    　View Summary

    Revisiting Kolmogorov's scaling laws and Onsager's conjecture, we made an assessment of their mathematical relevance from the view point of stochastic processes. Then we employed the Karman-Howarth-Monin relation as the energy dissipation rate to propose a new mathematical model of turbulence in the light of dissipative weak solutions of the incompressible Euler equations of which our sample space of turbulence consists. Besides, we conducted a numerical computation to verify the existence of a Gibbs measure on our sample space. We also investigated the blowup problem for the pseudo-conformally invariant nonlinear Schroedinger equations simultaneously. We established the loglog-law on the blowup rate for a class of blowup solutions by means of Nelson diffusions. Through out our project, we learned the importance of the use of our idea and method to be enhanced and to investigate other type of nonlinear PDEs, which led us to a new KAKENHI project continuing this attempt further.

  • Dynamics of the Gross-Pitaevskii equation and related problems

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Young Scientists (B)

    Project Year :

    2012.04
    -
    2015.03
     

    FUKUIZUMI Reika

    　View Summary

    The Gross-Pitaevskii equation perturbed by (only temporal) white noise is considered. In particular, we analyzed the modulation parameters in a stable vortex solution and we estimated how long those modulation parameters can have a meaning compared to the noise, that is, how long the stable vortex input initially can persist its form compared to the strength of the noise. On the other hand, with the use of semi-classical technique, we justified the approximation of the wave function of the Gross-Pitaevskii equation trapped in a periodic potential via the solution of the associated discrete nonlinear Schroedinger equation. As an application of this approximation, we showed the localization of the wave function even if defocusing nonlinearities are considered.

  • Quantum stochastic analysis - Transforms and spectral analysis

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)

    Project Year :

    2011.04
    -
    2015.03
     

    OBATA Nobuaki, FUKUIZUMI Reika, HASEGAWA Takehisa, SEGAWA Etsuo, KUBO Hideo, HIAI Fumio, SUZUKI Kanako

    　View Summary

    For the development of quantum stochastic analysis we focused on 'quantum white noise calculus' from analytic aspect and 'spectral analysis of complex networks' from algebraic aspect. We aimed at the establishment of the mathematical fundamentals and the paradigm for collaborating with other research fields for applications. By means of quantum white noise calculus, the Bogoliubov transform and the Girsanov transform are characterized by the white noise differential equations of new types. A quantum probabilistic method is applied to the spectral analysis of digraphs such as Manhattan product. The phase transition of various dynamics on networks is studied in detail with the help of numerical computation. New statistical properties of quantum walks on graphs such as localization are obtained by generalizing the existing method of spectral analysis.

  • ボース・アインシュタイン凝縮のモデル方程式のダイナミクス

    日本学術振興会  日仏交流促進事業<SAKURA>共同研究(仏外務省)

    Project Year :

    2010.04
    -
    2012.03
     

    福泉 麗佳

  • Stability of solitary waves for nonlinear dispersive equations

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research

    Project Year :

    2009.04
    -
    2012.03
     

    FUKUIZUMI Reika

    　View Summary

    Concerning a model for the Bose-Einstein Condensation trapped under an optical confinement involving fluctuations by laser frequencies, I justified mathematically the existence of solution constructing the fundamental solution of linear stochastic Schrodinger equations, and proved a long time behavior of stable standing waves influenced by temporal white noise. On the other hand, I investigated the stability of excited states for a model which describes the propagation of laser beam in the hollow-core fibers. As for a model of optic fibers, I showed the symmetry breaking of ground state for the case where two symmetric defects are present in the medium.

  • Geometry and Analysis of Wave Fields

    Japan Society for the Promotion of Science  Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (S)

    Project Year :

    2004
    -
    2008
     

    OZAWA Tohru, ASAO Arai, GEN Nakamura, KIMITOSHI Tsutaya, REIKA Fukuizumi

  • 非線形分散型方程式の孤立波解の安定性について

    日本学術振興会  科学研究費助成事業 若手研究(B)

    Project Year :

    2005
    　
    　
     

    福泉 麗佳

    　View Summary

    (i)
    次ページの論文[2][4]において,非一様媒質の光導波管を表す非線形シュレディンガー方程式の定在波解の安定性及び不安定性の考察をした.ここでいう安定性とは.定在波解に小さな摂動を加えて時間発展させても、やはり定在波解に近い状態であり続けるという意味であるが,定在波解の安定性が,非一様媒質の屈折率を表す関数の,遠方での減衰オーダーや.原点での特異性のオーダーに依存する事を明らかにした.
    さらに,一様な媒質を考えた場合と比較すると,定在波解が不安定になりやすいということがわかった.非一様媒質における非線形シュレディンガー方程式の定在波解の安定性の研究は,1980年代後半にAkhmediev, Jones, Grillakis, Shatahand Straussらによって3層媒質という特別な場合について分岐理論を用いて調べられていたが,一般的な媒質の場合に分岐理論を適用しようとすると,考え得る非線形構造に制限がかかってしまう.そこで,より一般的な媒質に関して調査した.より一般的な媒質を考えることで,方程式の持つスケール不変性が崩れるため,定在波の振動数に関する漸近的な解析手段を応用し,問題解決を図った.
    (ii)
    非線形楕円型方程式の解について,複素数値関数の解の指数減衰とそのシャープな減衰オーダーについて考察した(論文[1][3]).
    このような減衰オーダーは今までの手法では,常微分的な方法に頼っていたため取り扱う解が正値球対称であることが必要であった.しかし部分積分を基本にした非常に簡潔な証明によってより一般的な解についても適用できるよう拡張した.

  • 非線形分散型方程式の孤立波解の安定性と不安定性

    日本学術振興会  科学研究費助成事業 特別研究員奨励費

    Project Year :

    2002
    -
    2004
     

    福泉 麗佳

    　View Summary

    今年度の最も主要な成果は,非線形項が臨界冪の場合に,調和ポテンシャルのようなポテンシャル項を伴う非線形シュレディンガー方程式の定在波解が安定であることを証明したことである.ポテンシャル項が伴わない場合には,20年ほど前にWeinsteinによって,臨界冪の場合は定在波解は爆発の意味で不安定になることが示されていた.したがって,臨界冪の場合は,今回の結果により,ポテンシャル項の有無が安定・不安定性の問題に大きく影響することがわかった.この事実は,Rose and Weinsteinによる数値実験で予想はされていたが,はじめて数学的にも解明できたことになる.また,昨年度の継続として,非一様媒質の光導波管を表す非線形シュレディンガー方程式についての考察をし,定在波解の安定性が,非一様媒質の屈折率を表す関数の,遠方での減衰オーダーや,原点での特異性のオーダーに依存する事を明らかにした.非一様媒質における非線形シュレディンガー方程式の定在波解の安定性の研究は,1980年代後半にAkhmediev, Jones, Grillakis, Shatah and Straussらによって3層媒質という特別な場合について分岐理論を用いて調べられていたが,一般的な媒質の場合に分岐理論を適用しようとすると,考え得る非線形構造に制限がかかってしまう.そこで,より一般的な媒質に関して調査した.この問題については,10月から1月にかけてフランスの南パリ大学に滞在し,その大学のスタッフと議論することで結果を昨年のものより発展させることができた.さらには,非線形楕円型方程式の解について,複素数値関数の解の指数減衰とそのシャープな減衰オーダーについて考察もした.このような減衰オーダーは今までの手法では,常微分的な方法に頼っていたため,取り扱う解が正値球対称であることが必要であった.今回は全く異なる方法によって,より一般的な解についても適用できるよう拡張した.

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Misc

  • Renormalization of a 1d quadratic Schrodinger model with additive noise

    Aurelien Deya, Reika Fukuizumi and Laurent Thomann

       2023.04

    DOI

  • 基底状態のエネルギーを最小化する空間分割

    一木輝久, 坂口茂, 福泉麗佳

    一般社団法人日本物理学会第74回年次大会(2019)日本物理学会講演概要集    2019.03

    DOI

 

Syllabus

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Teaching Experience

  • 解析学概論C(関数解析)

    宮城教育大学  

    2022.04
    -
    2022.09
     

  • 数学特別講義（集中講義）

    京都大学大学院理学研究科数学教室  

    2019.04
    -
    2020.03
     

  • 大学院確率論特別講義Ⅱ

    名古屋大学大学院多元数理科学研究科  

    2014.04
    -
    2015.03
     

  • Introduction aux Equations aux Derivees Partielles

    ENSAE ParisTech  

    2009.09
    -
    2010.08
     

  • フレッシュマンセミナー金融・証券のための数学

    北海道大学  

    2008.04
    -
    2008.09
     

 

Social Activities

  • 理数科・模擬講義

    静岡県立清水東高等学校 

    2023.11
    　
    　

  • 量子の世界における流れの数学

    早稲田大学  オープンキャンパス模擬講義 

    2023.08
    　
    　

  • 量子の世界における流れと数学

    東京大学数理科学研究科  2022年度 駒場祭 公開講座「量子の世界の数学」 

    2022.11
    -
    　

  • 私の博士論文とその周辺

    数理女子事務局 

    2022.10
    -
    　

  • "量子の世界における流れの数学''

    東京大学数理科学研究科  東京大学数理科学研究科女子中高生向けイベント「数学の魅力」 

    2022.03
    -
    　

  • 2022年度 東北大学×アクサ協働プログラム 「保険数理セミナー」

    2022年度 東北大学×アクサ協働プログラム 「保険数理セミナー」 

    2022
    -
    　

  • 数学の世界へようこそ-超低温研究分野における数学の貢献-

    Tohoku University Association of Leading Women Researchers in Engineering (ALicE)  Women with Sparkle! 

    2020.09
    -
    　

  • 数学者って何？数学の研究を仕事にするとは？

    Tohoku University  2017年度東北大学男女共同参画セミナー～研究者ってなに？オープンキャンパス編～ 

    2017.07
    　
    　

  • La voie royale

    2005.01
    -
    　

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Academic Activities

  • French Japanese conference on Probability and Interactions

    Academic society, research group, etc.

    Thierry Bodineau, Charles Bordenave, Anne de Bouard, Arnaud Debussche, Benoit Collins, Reika Fukuizumi, Takashi Kumagai, Gregory Miermont, Tomohiro Sasamoto  

    2024.03
    　
    　

  • New trends in nonlinear dispersive equations

    Academic society, research group, etc.

    2024.01
    -
    　

  • 東北大学「幾何と解析セミナー」

    S. Sakaguchi, J. Takahashi, K. Funano, R. Fukuizumi  

    2015
    -
    2023.03

  • OCAMI 研究集会「量子流体における数理構造の解明」

    Academic society, research group, etc.

    福泉麗佳, 小林未知数, 坂上貴之, 坪田誠  

    2023.01
    　
    　

  • 東北大学「青葉山勉強会」

    Academic society, research group, etc.

    R.Fukuizumi with S. Sakaguchi  

    2013
    -
    2023

  • RIMS共同研究(公開型・女性推進型)「Nonlinear and Random Waves」

    Academic society, research group, etc.

    福泉麗佳, Anne de Bouard  

    2022.10
    　
    　

  • Reaction-Diffusion Equations

    Reika Fukuizumi, Goro Akagi, Shigeru Sakaguchi  

    2022.01
    -
    　

  • Tohoku University GSIS Online Lecture Series「Singular limit of deterministic and stochastic reaction-diffusion systems」

    Reika Fukuizumi, Goro Akagi, Natsuhiko Yoshinaga  

    2021.11
    -
    2022.01

  • Online Workshop "PDEs and Probability Theory-beyond boundaries-"

    2021.06
    　
    　

  • 大阪市立大学数学研究所Zoom研究会「量子渦と非線形波動」

    Reika Fukuizumi, Michikazu Kobayashi  

    2021.02
    　
    　

  • 東北大学大学院情報科学研究科 純粋・応用数学研究センター 第30回幾何と解析セミナー

    坂口茂，福泉麗佳，船野敬，高橋淳也  

    2020.02
    -
    　

  • 東北大学松鶴数学講究「Monotonicity methods for SPDE, including the time fractional case」

    Reika Fukuizumi, Y. Hariya  

    2019.11
    　
    　

  • 東北大学GSISサマースクール「The homogenization method for topology optimization of structures: old and new」

    Reika Fukuizumi  

    2018.08
    　
    　

  • Workshop ``Nonlinear Partial Differential Equations on Graphs',' at MFO, Germany

    Reika Fukuizumi, J. Marzuola, D. Pelinovsky and G. Schneider  

    2017.06
    　
    　

  • 東北大学GSISウインタースクール「Stochastic homogenization and its applications」

    2017.02
    　
    　

  • Nonlinear Wave and Dispersive equations, Kyoto 2016

    Reika Fukuizumi  

    2016.09
    　
    　

  • 東北大学GSISサマースクール「Homogenization and Numerical Analysis」

    Reika Fukuizumi  

    2015.07
    -
    2015.08

  • 2014年度確率解析シンポジウム「確率解析とその周辺」

    Reika Fukuizumi, S. Aida, I. Shigekawa, H. Kawabi, Y. Inahama and S. Kusuoka  

    2014.10
    　
    　

  • 日仏共同研究事業SAKURA 研究集会「１Stability problems in nonlinear dispersive PDEs」

    R.Fukuizumi with A. de Bouard, N. Tzvetkov  

    2010.04
    -
    2011.03

  • 2011年日仏共同研究事業SAKURA研究集会「Stability problems in nonlinear dispersive PDEs」

    Reika Fukuizumi, A. de Bouard and N. Tzvetkov  

    2011
    -
    　

  • 7th AIMS International Conference on Dyn. Systems, Diff. Equations and Applications

    Reika Fukuizumi, H. Chen and M. Colin  

    2008.05
    　
    　

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Sub-affiliation

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Research Institute

  • 2023
    -
    2024

    Waseda Research Institute for Science and Engineering   Concurrent Researcher