Graduate School of Science and Engineering（Engineering）
理工学専攻（情報工学）
日本語
Update date：2024/12/23
Associate Professor
Morioka Hisashi

Research History

  1. 2011/04-2013/03JSPS Research FellowDC2
  2. 2013/04-2014/03Division of Mathematics, University of TsukubaReseach Fellow
  3. 2013/04-2014/03Faculty of Science, Gakushuin UniversityResearch Fellow
  4. 2013/04-2014/08Shibaura Institute of TechnologyCollege of EngineeringPart-time Lecturer
  5. 2013/10-2014/08The University of Electro-CommunicationsFaculty of Informatics and EngineeringPart-time Lecturer
  6. 2014/04-2014/08Gakushuin UniversityDepartment of MathematicsPart-time Lecturer
  7. 2014/09-2016/09Shibaura Institute of TechnologyCenter for Promotion of Educational InnovationLecturer
  8. 2016/10-2019/03Doshisha UniversityFaculty of Science and Engineering, Department of Energy and Mechanical EngineeringAssistant Professor
  9. 2017/04-2017/08The university of Shiga prefectureSchool of engineeringPart-time Lecturer
  10. 2019/04-2022/03Ehime UniversityGraduate School of Science and Engineering (Electrical and Electronic Engineering and Computer Science)Senior Assistant Professor
  11. 2020/04-presentEhime UniversityCenter for Data Science
  12. 2021/07-2021/11Human Resource Association of MathematicsPart-time Lecturer
  13. 2022/04-presentEhime UniversityGraduate School of Science and Engineering Electrical and Electronic Engineering and Computer ScienceAssociate Professor

Education

  1. University of Tsukuba2008/042010/03
  2. University of Tsukuba2010/042013/03

Degree

  1. Master in EducationUniversity of Tsukuba2010/03
  2. Ph.D in ScienceUniversity of Tsukuba2013/03

Research Areas

  1. Scattering theory
  2. Spectral theory
  3. Inverse problem
  4. Quantum walk

Research Interests

  1. scattering matrix
  2. Schrödinger operator
  3. discrete Schrödinger operator
  4. quantum walk
  5. spectral theory
  6. graph theory
  7. inverse problem
  8. discrete Laplacian
  9. Laplacian
  10. scattering theory

Research Projects

  1. Japan Society for the Promotion of ScienceGrants-in-Aid for Scientific ResearchSpectral theory and semi-classical analysis for unitary operators and its application to studies of resonancesScientific Research (C)2024/04-2028/03Principal investigator
  2. Japan Society for the Promotion of ScienceGrant-in-aidユニタリ作用素に対するスペクトル理論の研究と散乱理論への応用Grant-in-aid for young scientists2020/04-2024/03Principal investigator
  3. Japan Society for the Promotion of ScienceGrant-in-Aid for Young Scientists (B)Scattering theory on manifolds and graphs via geometric perturbations and nonhomogeneous medium2016/04-2020/03Principal investigator
  4. Japan Society for the Promotion of ScienceGrant-in-Aid for JSPS Fellows結晶格子における離散シュレディンガー作用素の逆問題と連続体極限2011/04-2013/03Principal investigator
  5. 筑波大学若手研究者育成事業 つくばダイアモンド研究奨励費正方格子におけるSchrödinger作用素のスペクトルと逆問題2010-2011Principal investigator
View details...

Books and Other Publications

  1. データサイエンティスト教程 基礎II 現代数学の指標編集:鈴木 貴 編集委員:高野 渉 朝倉暢彦 中澤 嵩 下川和郎 江口翔一 森岡 悠編集委員学術図書出版社2023/069784780611564URL
View details...

Papers

  1. A remark on the absence of eigenvalues in continuous spectra for discrete Schrödinger operators on periodic lattices2024/11Kazunori Ando Hiroshi Isozaki Hisashi Moriokapreprint(MISC) Institution technical report and pre-print, etc.10.48550/arXiv.2411.03577We prove a Rellich-Vekua type theorem for Schrödinger operators with exponentially decreasing potentials on a class of lattices containing square, triangular, hexagonal lattices and their ladders. We also discuss the unique continuation theorem and the non-existence of eigenvalues embedded in the continuous spectrum.
  2. Complex translation methods and its application to resonances for quantum walks2024/04Kenta Higuchi Hisashi MoriokaReviews in Mathematical Physics36, 1-28Research paper (scientific journal)10.1142/S0129055X24500181In this paper, some properties of resonances for multi-dimensional quantum walks are studied. Resonances for quantum walks are defined as eigenvalues of complex translated time evolution operators in the pseudo momentum space. For some typical cases, we show some results of existence or nonexistence of resonances. One is a perturbation of an elastic scattering of a quantum walk which is an analogue of classical mechanics. Another one is a shape resonance model which is a perturbation of a quantum walk with a non-penetrable barrier.
  3. Resonance expansion for quantum walks and its applications to the long-time behavior2024/04Kenta Higuchi Hisashi Morioka Etsuo SegawaJournal of Spectral Theory14/ 1, 207-244Research paper (scientific journal)10.4171/JST/494In this paper, resonances are introduced to a class of quantum walks on $\mathbb{Z}$. Resonances are defined as poles of the meromorphically extended resolvent of the unitary time evolution operator. In particular, they appear inside the unit circle. Some analogous properties to those of quantum resonances for Schrödinger operators are shown. Especially, the resonance expansion, an analogue of the eigenfunction expansion, indicates the long-time behavior of quantum walks. The decaying rate, the asymptotic probability distribution, and the weak limit of the probability density are described by resonances and associated (generalized) resonant states. The generic simplicity of resonances is also investigated.
  4. Scattering theory for waves and eigenvalue problems based on inverse scattering2024/03Hisashi MoriokaBulletin of the Japan Society for Industrial and Applied Mathematics34/ 1, 5-15Research paper (scientific journal)10.11540/bjsiam.34.1_5Japan Society for Industrial and Applied MathematicsIn this study, we review some topics on spectral and scattering theory for Schrödinger operators or time-independent wave equations and inverse scattering problems. First, we consider an example of an inverse problem for a one-dimensional wave equation with a piecewise constant coefficient. Nonscattering energy naturally appears in the process of reconstruction of the coefficient. A similar problem is known in multidimensional cases. This problem can be reduced to an interior transmission eigenvalue problem. Furthermore, herein, we refer to the shape resonance model for the Schrödinger equation as a related topic.
  5. Comfortable place for quantum walkers on finite path2022/07/16Yoshihiro Anahara Norio Konno Hisashi Morioka Etsuo SegawaQuantum Information Processing21, 1-15Research paper (scientific journal)10.1007/s11128-022-03588-5We consider the stationary state of a quantum walk on the finite path, where the sink and source are set at the left and right boundaries. The quantum coin is uniformly placed at every vertex of the path graph. At every time step, a new quantum walker penetrates into the internal from the left boundary and also some existing quantum walkers in the internal goes out to the sinks located in the left and right boundaries. The square modulus of the stationary state at each vertex is regarded as the comfortability for a quantum walker to this vertex in this paper. We show the weak convergence theorem for the scaled limit distribution of the comfortability in the limit of the length of the path.
View details...

Presentations

  1. 量子ウォークの共鳴極を用いた共鳴トンネル効果および快適性の解析日本応用数理学会環瀬戸内応用数理研究部会2024/12/21Oral presentation(general)URL
  2. 障害物がある場合の波動方程式の数値計算とその応用日本応用数理学会環瀬戸内応用数理研究部会2024/12/21Oral presentation(general)URL
  3. 波動方程式の逆散乱による超音波物質同定問題の基礎研究日本応用数理学会2024年度年会, 正会員OS「逆問題および非適切問題の数理解析とその応用」2024/09/16Oral presentation(general)URL
  4. A study on bond correction methods via inverse scattering for 1D elastic wave equationsFinland-Japan Workshop in Industrial and Applied Mathematics2024/08/29Oral presentation(invited, special)URLJoint work with Steeve Gréaux (Ehime University, GRC).
  5. 波動方程式の逆散乱による超音波物質同定問題の基礎研究南大阪応用数学セミナー2024/06/29Public discourse, seminar, tutorial, course, lecture and othersURL鉱物や岩石の物質特性を超音波による非破壊検査で決定する実験においては, パルス状の入射波に対し, 反射波を計測し,標本長と伝播時間の関係から標本固有の波速度を決定する. この際, 実験系のスケールでは, 標本を実験装置に固定するための接合材層(bond)による影響を無視できない. この影響を補正するため, 従来 bond correction method と呼ばれる方法が用いられているが, この定式化には数学的に疑問の余地があり, また実験的にも今日に至るまで補正手段の検討が続けられている.最近, 数物協働で波動方程式による解析に基づいてこの補正法の再検討を始めており, 本講演では現状についてご報告したい.
View details...

Allotted Class

  1. 2024Fundamental Computer Science
  2. 2024Fundamental Computer Science
  3. 2024Fundamental Computer Science
  4. 2024Fundamental Computer Science
  5. 2024Fundamental Computer Science
View details...

Textbooks and Teaching Materials

  1. Lecture not for Advanced Applied Mathematics I2020/04/12We study some basic topics of inverse problems in mathematical point of view. Inverse problems appear in various fields of engineering. A typical problem is to determine an unknown system from a set of datum of inputs and outputs. Inverse problems are often ill-posed. Namely, they are unstable in view of errors and noises in datum, or solutions of inverse problems can not be determined uniquely from a measurement which we can get practically. Then we need the mathematical analysis in order to deal with the ill-posedness.
View details...

Social Activities

  1. Human Resource Association of Mathematics, Part-time Lecturer2021/07-2021/11
View details...

Professional Memberships

  1. 2022/10-presentThe Inverse Problems International Association
  2. 2022/07-presentThe Japan Society for Industrial and Applied Mathematics
  3. 2010/10-presentThe Mathematical Society of Japan
View details...

Teaching Experience

  1. Applied Mathematics IIFaculty of Engineering, Ehime University2024/09-present
  2. Fundamentals of Applied MathematicsGraduate School of Science and Engineering, Ehime University2023/12-present
  3. Probability and StatisticsFaculty of Engineering, Ehime University2023/04-present
  4. Differential and Integral Calculus IIFaculty of Engineering, Ehime University2021/10-2023/02
  5. Linear Algebra IIThe University of Electro-Communications2013/10-2014/02
View details...