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Algebraic approaches to strongly correlated electron systems

Research Project

Project/Area Number 23740298
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionGakushuin University

Principal Investigator

KATSURA HOSHO  学習院大学, 理学部, 准教授 (80534594)

Project Period (FY) 2011 – 2013
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords強相関電子系 / 物性基礎論 / 数理物理 / エンタングルメント / 記号計算
Research Abstract

We have studied a variety of lattice models that describe systems of strongly interacting fermions, bosons, and spins. Examples of the models include Bose- and Fermi-Hubbard models, and the quantum hard-square model. Various exact and/or rigorous results were obtained by exploiting the integrability or using some mathematical tools like the Perron-Frobenius theorem. For example, we have proved a natural analogue of Nagaoka's theorem in the SU(n) Hubbard model. We have also studied entanglement spectra of solvable lattice models in two dimensions by combining analytical and numerical techniques. The results obtained suggest that the entanglement Hamiltonian of the valence-bond-solid (VBS) state is well described by the one-dimensional Heisenberg model.

Report

(4 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (73 results)

All 2014 2013 2012 2011 Other

All Journal Article (21 results) (of which Peer Reviewed: 19 results) Presentation (45 results) (of which Invited: 15 results) Remarks (7 results)

  • [Journal Article] Composite-kink solutions of coupled nonlinear wave equations2014

    • Author(s)
      H. Katsura
    • Journal Title

      Phys. Rev. D

      Volume: 89 Issue: 8 Pages: 0850191-5

    • DOI

      10.1103/physrevd.89.085019

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Existence of an energy gap in a one-dimensional Lesanovsky model2013

    • Author(s)
      H. Katsura
    • Journal Title

      Phys. Rev. A

      Volume: 88 Issue: 6

    • DOI

      10.1103/physreva.88.065602

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Phase diagram and pair Tomonaga-Luttinger liquid in a Bose-Hubbard model with flat bands2013

    • Author(s)
      S. Takayoshi, H. Katsura, N. Watanabe, and H. Aoki
    • Journal Title

      Phys. Rev. A

      Volume: 88 Issue: 6

    • DOI

      10.1103/physreva.88.063613

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Ground-state Energies of Spinless Free Fermions and Hard-core Bosons2013

    • Author(s)
      Wenxing Nie, Hosho Katsura, Masaki Oshikawa
    • Journal Title

      Phys. Rev. Lett.

      Volume: 111 Issue: 10 Pages: 1004021-5

    • DOI

      10.1103/physrevlett.111.100402

    • Related Report
      2013 Annual Research Report 2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] 量子力学と恒等式2013

    • Author(s)
      桂 法称
    • Journal Title

      数理科学

      Volume: vol.600 Pages: 14-20

    • URL

      http://www.saiensu.co.jp/?page=book_details&ISBN=4910054690637&YEAR=2013

    • Related Report
      2013 Final Research Report
  • [Journal Article] Ground States of the Spin-1 Bose-Hubbard Model2013

    • Author(s)
      H. Katsura and H. Tasaki
    • Journal Title

      Phys. Rev. Lett

      Volume: 110 Issue: 13

    • DOI

      10.1103/physrevlett.110.130405

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nagaoka states in the SU(n) Hubbard model2013

    • Author(s)
      H. Katsura and A. Tanaka
    • Journal Title

      Phys. Rev. A

      Volume: 87 Issue: 1

    • DOI

      10.1103/physreva.87.013617

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] 量子統計力学と恒等式2013

    • Author(s)
      桂 法称
    • Journal Title

      数理科学

      Volume: 600 Pages: 14-20

    • Related Report
      2013 Annual Research Report
  • [Journal Article] Interacting Fibonacci anyons in a Rydberg gas2012

    • Author(s)
      I. Lesanovsky and H. Katsura
    • Journal Title

      Phys. Rev. A

      Volume: 86 Issue: 4

    • DOI

      10.1103/physreva.86.041601

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Entanglement Spectra of the quantum hard-square model : Holographic minima models2012

    • Author(s)
      Shu Tanaka, Ryo Tamura, Hosho Katsura
    • Journal Title

      Physical Review A

      Volume: 86 Issue: 3 Pages: 0323261-9

    • DOI

      10.1103/physreva.86.032326

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Multifractals competing with solitons on Fibonacci optical lattices2012

    • Author(s)
      M. Takahashi, H. Katsura, M. Kohmoto, and T. Koma
    • Journal Title

      New J. Phys

      Volume: 14 Issue: 11 Pages: 113012-113012

    • DOI

      10.1088/1367-2630/14/11/113012

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Theory of Raman Scattering in One-Dimensional Quantum Spin-1/2 Antiferromagnets2012

    • Author(s)
      M. Sato, H. Katsura, and N. Nagaosa
    • Journal Title

      Phys. Rev. Lett

      Volume: 108 Issue: 23

    • DOI

      10.1103/physrevlett.108.237401

    • Related Report
      2013 Final Research Report 2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] エネルギー・スケール変調による量子系の境界条件・トポロジーの制御2012

    • Author(s)
      引原俊哉,桂 法称,丸山 勲,西野友年
    • Journal Title

      日本物理学会誌

      Volume: 67, No.6 Pages: 394-394

    • NAID

      10030864389

    • URL

      http://www.jps.or.jp/books/gakkaishi/2012/06/67-06.html

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Sine-square deformation of solvable spin chains and conformal field theories2012

    • Author(s)
      H. Katsura
    • Journal Title

      J. Phys. A : Math. Theor

      Volume: 45 Issue: 11 Pages: 115003-115003

    • DOI

      10.1088/1751-8113/45/11/115003

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] General Relationship between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States2012

    • Author(s)
      X-L. Qi, H. Katsura, and A. W. W. Ludwig
    • Journal Title

      Phys. Rev. Lett

      Volume: 108 Issue: 19

    • DOI

      10.1103/physrevlett.108.196402

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] エネルギー・スケール変調による量子系の境界条件・トポロジーの制御2012

    • Author(s)
      引原俊哉,桂 法称,丸山 勲,西野友年
    • Journal Title

      日本物理学会誌

      Volume: 67 Pages: 394-397

    • NAID

      10030864389

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Effect of lattice geometry on magnon Hall effect in ferromagnetic insulators2011

    • Author(s)
      T.Ideue, Y.Onose, H.Katsura, Y.Shiomi, S.Ishiwata, N.Nagaosa, and Y
    • Journal Title

      Tokura Physical Review B

      Volume: 85 Issue: 13 Pages: 134411-134411

    • DOI

      10.1103/physrevb.85.134411

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Entanglement Spectra of the Two-Dimensional Affleck-Kennedy-Lieb-Tasaki Model : Correspondence between the Valence-Bond-Solid State and Conformal Field Theory2011

    • Author(s)
      Jie Lou, Shu Tanaka, Hosho Katsura, Naoki Kawashima
    • Journal Title

      Physical Review B

      Volume: 84 Issue: 24 Pages: 245128-245128

    • DOI

      10.1103/physrevb.84.245128

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sine-square deformation of free fermion systems in one and higher dimensions2011

    • Author(s)
      I.Maruyama, H.Katsura, T.Hikihara
    • Journal Title

      Phys.Rev.B

      Volume: 84 Issue: 16

    • DOI

      10.1103/physrevb.84.165132

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Nearly Flatbands with Nontrivial Topology2011

    • Author(s)
      K. Sun, Z-C. Gu, H. Katsura, and S. Das Sarma
    • Journal Title

      Phys. Rev. Lett

      Volume: 106 Issue: 23

    • DOI

      10.1103/physrevlett.106.236803

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] Exact ground state of the sine-square deformed XY spin chain2011

    • Author(s)
      H. Katsura
    • Journal Title

      J. Phys. A : Math. Theor

      Volume: 44 Issue: 25 Pages: 252001-252001

    • DOI

      10.1088/1751-8113/44/25/252001

    • Related Report
      2013 Final Research Report 2011 Research-status Report
    • Peer Reviewed
  • [Presentation] Laughlin 状態を記述する1次元格子模型における基底状態の一意性とエネルギーギャップの存在証明2013

    • Author(s)
      汪正元, 中村正明, 桂 法称
    • Organizer
      日本物理学会2013年秋季大会
    • Place of Presentation
      徳島大学(徳島)
    • Year and Date
      2013-09-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Ground-state Energies of Spinless Free Fermions and Hard-core Bosons on Infinite Lattice2013

    • Author(s)
      W-X. Nie, 桂 法称, 押川正毅
    • Organizer
      日本物理学会第68回年次大会
    • Place of Presentation
      広島大学(広島)
    • Year and Date
      2013-03-29
    • Related Report
      2013 Final Research Report
  • [Presentation] 量子hard-square模型の基底状態と励起ギャップ2013

    • Author(s)
      桂 法称
    • Organizer
      日本物理学会第68回年次大会
    • Place of Presentation
      広島大学(広島)
    • Year and Date
      2013-03-28
    • Related Report
      2013 Final Research Report
  • [Presentation] 2次元量子格子気体模型におけるエンタングルメント2013

    • Author(s)
      田中 宗, 田村 亮, 桂 法称
    • Organizer
      日本物理学会第68回年次大会
    • Place of Presentation
      広島大学(広島)
    • Year and Date
      2013-03-28
    • Related Report
      2013 Final Research Report
  • [Presentation] Interacting Rydberg atoms as quantum hard-squres2013

    • Author(s)
      H. Katsura
    • Organizer
      Workshop on Disordered and Topological Systems
    • Place of Presentation
      Zhejiang University, 杭州, 中国
    • Year and Date
      2013-03-18
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Inhomogeneous but solvable/integrable models2013

    • Author(s)
      H. Katsura
    • Organizer
      Infinite Analysis : Past, Present, and Future
    • Place of Presentation
      京都大学(京都)
    • Year and Date
      2013-03-04
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Inhomogeneous but solvable/integrable models2013

    • Author(s)
      桂 法称
    • Organizer
      Infinite Analysis: Past, Present and Future on the occasion of the retirement of Professor Tetsuji Miwa
    • Place of Presentation
      京都大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Interacting Rydberg atoms as quantum hard squares2013

    • Author(s)
      桂 法称
    • Organizer
      Workshop on Disordered and Topological Systems
    • Place of Presentation
      Zhejiang University, 杭州 (中国)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Ground-state Energies of Spinless Free Fermions and Hard-core Bosons on Infinite Lattice2013

    • Author(s)
      Wenxing Nie
    • Organizer
      日本物理学会第68回年次大会
    • Place of Presentation
      広島大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 量子hard-square模型の基底状態と励起ギャップ2013

    • Author(s)
      桂 法称
    • Organizer
      日本物理学会第68回年次大会
    • Place of Presentation
      広島大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 2次元量子格子気体模型におけるエンタングルメント2013

    • Author(s)
      田中宗
    • Organizer
      日本物理学会第68回年次大会
    • Place of Presentation
      広島大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Sine-square deformation of one-dimensional critical systems2012

    • Author(s)
      H. Katsura
    • Organizer
      Novel Development of Statistical Physics
    • Place of Presentation
      東京大学(東京)
    • Year and Date
      2012-12-04
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Entanglement spectra of two-dimensional solvable models2012

    • Author(s)
      H. Katsura
    • Organizer
      Entanglement Spectra in Complex Quantum Wavefunctions, MPIPKS
    • Place of Presentation
      Dresden, Germany
    • Year and Date
      2012-11-16
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Li-Haldane予想とVBS/CFT対応2012

    • Author(s)
      桂 法称
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学(神奈川)
    • Year and Date
      2012-09-19
    • Related Report
      2013 Final Research Report
  • [Presentation] ハードコア格子ガスモデルにおけるエンタングルメント・スペクトル2012

    • Author(s)
      田中 宗, 田村 亮, 桂 法称
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学(神奈川)
    • Year and Date
      2012-09-19
    • Related Report
      2013 Final Research Report
  • [Presentation] Rydberg Blockadeを用いたFibonacciエニオンの実現2012

    • Author(s)
      桂 法称, Igor Lesanovsky
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学(神奈川)
    • Year and Date
      2012-09-18
    • Related Report
      2013 Final Research Report
  • [Presentation] SU(n)ハバード模型における長岡状態2012

    • Author(s)
      桂 法称, 田中彰則
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学(神奈川)
    • Year and Date
      2012-09-18
    • Related Report
      2013 Final Research Report
  • [Presentation] Entanglement spectra of two-dimensional solvable models2012

    • Author(s)
      H. Katsura
    • Organizer
      Correlations and Entanglement in Many-body Systems Out of Equilibrium
    • Place of Presentation
      精華大学, 新竹市, 台湾
    • Year and Date
      2012-09-11
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Golden chain of strongly interacting Rydberg atoms2012

    • Author(s)
      H. Katsura
    • Organizer
      APCTP Focus Program on Quantum Condensation(QC12), APCTP
    • Place of Presentation
      Pohang, Korea
    • Year and Date
      2012-08-21
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Symmetry and self-duality in discrete-time quantum walks2012

    • Author(s)
      桂 法称
    • Organizer
      CMRU 研究会「量子確率論と量子ウォーク」
    • Place of Presentation
      東北大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Golden chain of strongly interacting Rydberg atoms2012

    • Author(s)
      桂 法称
    • Organizer
      APCTP Focus Program on Quantum Condensation (QC12)
    • Place of Presentation
      Asia Pacific Center for Theoretical Physics, Pohang (Korea)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Entanglement spectra of two-dimensional solvable models2012

    • Author(s)
      桂 法称
    • Organizer
      Correlations and Entanglement in Many-body Systems Out of Equilibrium
    • Place of Presentation
      精華大学(台湾)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Entanglement spectra of two-dimensional solvable models2012

    • Author(s)
      桂 法称
    • Organizer
      Entanglement Spectra in Complex Quantum Wavefunctions
    • Place of Presentation
      MPIPKS, Dresden (Germany)
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Sine-square deformations of one-dimensional critical systems2012

    • Author(s)
      桂 法称
    • Organizer
      Novel Development of Statistical Physics
    • Place of Presentation
      東京大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Rydberg Blockadeを用いたFibonacciエニオンの実現2012

    • Author(s)
      桂 法称
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学
    • Related Report
      2012 Research-status Report
  • [Presentation] SU(n)ハバード模型における長岡状態2012

    • Author(s)
      田中彰則
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Li-Haldane予想とVBS/CFT対応2012

    • Author(s)
      桂 法称
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学
    • Related Report
      2012 Research-status Report
  • [Presentation] 1次元量子スピン鎖のラマン散乱におけるスピノン、ソリトン、ブリーザー励起2012

    • Author(s)
      佐藤正寛
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学
    • Related Report
      2012 Research-status Report
  • [Presentation] ハードコア格子ガスモデルにおけるエンタングルメント・スペクトル2012

    • Author(s)
      田中宗
    • Organizer
      日本物理学会2012年秋季大会
    • Place of Presentation
      横浜国立大学
    • Related Report
      2012 Research-status Report
  • [Presentation] トポロジカルな相におけるエンタングルメントと境界(石橋)状態2012

    • Author(s)
      桂 法称
    • Organizer
      第67回日本物理学会年次大会
    • Place of Presentation
      関西学院大学
    • Related Report
      2011 Research-status Report
  • [Presentation] From entanglement entropy to entanglement spectrum : 1+1D CFT embedded in 2D valence bond solid2011

    • Author(s)
      Jie Lou, 田中 宗, 桂 法称, 川島直輝
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学(富山)
    • Year and Date
      2011-09-23
    • Related Report
      2013 Final Research Report
  • [Presentation] 1次元量子磁性体におけるラマン散乱理論2011

    • Author(s)
      佐藤正寛, 桂 法称, 永長直人
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学(富山)
    • Year and Date
      2011-09-22
    • Related Report
      2013 Final Research Report
  • [Presentation] Nearly flat band with nontrivial topology2011

    • Author(s)
      K. Sun, Z-C. Gu, 桂 法称, S. Das Sarma
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学(富山)
    • Year and Date
      2011-09-22
    • Related Report
      2013 Final Research Report
  • [Presentation] 可解スピン鎖・場の理論におけるsine変形2011

    • Author(s)
      桂 法称
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学(富山)
    • Year and Date
      2011-09-21
    • Related Report
      2013 Final Research Report
  • [Presentation] Thermal Hall effect of magnons2011

    • Author(s)
      H. Katsura
    • Organizer
      International Discussion Meeting on Thermoelectrics and Related Materials
    • Place of Presentation
      Aalto University, Helsinki, Finland
    • Year and Date
      2011-06-15
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Entanglement spectrum of valence-bond-solid states : VBS/CFT correspondence2011

    • Author(s)
      H. Katsura
    • Organizer
      The 5th Asia Pacific Workshop on Quantum Information Science
    • Place of Presentation
      NTU, Singapore
    • Year and Date
      2011-05-28
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Entanglement spectrum of valence-bond-solid states: VBS/CFT correspondence2011

    • Author(s)
      桂 法称
    • Organizer
      THE 5th ASIA PACIFIC WORKSHOP ON QUANTUM INFORMATION SCIENCE IN CONJUNCTION WITH THE KOREPIN FESTSCHRIFT(招待講演)
    • Place of Presentation
      NTU, Singapore (Singapore)
    • Related Report
      2011 Research-status Report
  • [Presentation] Thermal Hall effect of magnons2011

    • Author(s)
      桂 法称
    • Organizer
      International Discussion Meeting on Thermoelectrics and Related Functional Materials(招待講演)
    • Place of Presentation
      Aalto University, Helsinki (Finland)
    • Related Report
      2011 Research-status Report
  • [Presentation] 可解量子スピン鎖・場の理論におけるsine変形2011

    • Author(s)
      桂 法称
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Nearly flat band with nontrivial Chern number2011

    • Author(s)
      桂 法称
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 1次元磁性体における量子ダイナミクスとラマン散乱の理論2011

    • Author(s)
      佐藤正寛
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Fibonacci 格子上の極低温原子気体の数値解析2011

    • Author(s)
      高橋雅裕
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Localization in Inhomogeneous Quantum Walks with Self-Duality2011

    • Author(s)
      鹿野豊
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Related Report
      2011 Research-status Report
  • [Presentation] From entanglement entropy to entanglement spectrum:1+1D CFT embedded in 2D valence bond solid2011

    • Author(s)
      Jie Lou
    • Organizer
      日本物理学会2011年秋季大会
    • Place of Presentation
      富山大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Thermal Hall Effect in Ferromagnetic Insulators2011

    • Author(s)
      桂 法称
    • Organizer
      26th International Conference on Low Temperature Physics
    • Place of Presentation
      Beijing International Convention Center , 北京(中国)
    • Related Report
      2011 Research-status Report
  • [Remarks]

    • URL

      http://www-cc.gakushuin.ac.jp/~20100072/

    • Related Report
      2013 Final Research Report
  • [Remarks] Hosho Katsura's Home Page

    • URL

      http://www-cc.gakushuin.ac.jp/~20100072/

    • Related Report
      2013 Annual Research Report
  • [Remarks] Publications

    • URL

      http://www-cc.gakushuin.ac.jp/~20100072/publication.html

    • Related Report
      2013 Annual Research Report
  • [Remarks] Hosho Katsura's Home Page

    • URL

      http://www-cc.gakushuin.ac.jp/~20100072/

    • Related Report
      2012 Research-status Report
  • [Remarks] Publications

    • URL

      http://www-cc.gakushuin.ac.jp/~20100072/publication.html

    • Related Report
      2012 Research-status Report
  • [Remarks]

    • URL

      http://www-cc.gakushuin.ac.jp/~20100072/

    • Related Report
      2011 Research-status Report
  • [Remarks]

    • URL

      http://www-cc.gakushuin.ac.jp/~20100072/publication.html

    • Related Report
      2011 Research-status Report

URL: 

Published: 2011-08-05   Modified: 2019-07-29  

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