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Theory of Superfluidity in inhomogeneous Bose systems

Research Project

Project/Area Number 21540352
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Condensed matter physics II
Research InstitutionThe University of Tokyo

Principal Investigator

KATO Yusuke  東京大学, 大学院・総合文化研究科, 准教授 (20261547)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords超低温 / 量子凝縮系 / 超固体 / ジョゼフソン効果 / 障害物ポテンシャル / 非古典的回転慣性 / 永久流 / グロス・ピタエフスキー方程式 / ボゴリューボフ方程式 / ポモー・リカ模型 / 固体超流動 / 臨界速度 / ソリトン / サドルノード分岐 / スケーリング則 / 相転移 / 超流動 / 固体 / ボース凝縮 / グロスピクエフスキー方程式 / スペクトル関数
Research Abstract

Superfluidity, which implies macroscopic flow without dissipation, is realized in quantum liquids with Bose-Einstein condensates. Supersolids, on the other hand, are quantum solids with superfluid property. While earlier studies have concluded that supersolidity is impossible in the presence of an obstacle, we have given a counter-example in the present research project. We have demonstrated that quantum solids can maintain supersolidity in the presence of obstacles through the Josephson effect.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (68 results)

All 2012 2011 2010 2009 Other

All Journal Article (16 results) (of which Peer Reviewed: 15 results) Presentation (46 results) Book (2 results) Remarks (4 results)

  • [Journal Article] Dynamics of One-dimensional Supersolids2012

    • Author(s)
      KUNIMI MASAYA, KOBAYASHI MICHIKAZU, KATO YUSUKE
    • Journal Title

      J. Phys. Conf. Proc.

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Anomalous Tunneling of Spin Wave in Polar State of Spin-1 BEC2012

    • Author(s)
      Watabe S., Kato, Y., Ohashi, Y.
    • Journal Title

      Journal of Physics : Conference series

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Anomalous Tunneling of Spin Wave in Heisenberg Ferromagnet2012

    • Author(s)
      Kato, Y., Watabe S., Ohashi, Y.
    • Journal Title

      Journal of Physics : Conference series

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dynamics of one-dimensional supersolids2012

    • Author(s)
      Kunimi M., Kobayashi M., Kato, Y.
    • Journal Title

      Journal of Physics : Conference series

      Volume: (掲載決定)

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Josephson effects in one-dimensional supersolids2011

    • Author(s)
      KUNIMI MASAYA, NAGAI YUKI, KATO YUSUKE
    • Journal Title

      Physical Review B

      Volume: Vol.84

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Josephson effects in one-dimensional supersolids2011

    • Author(s)
      Masaya Kunimi, Yuki Nagai, Yusuke Kato
    • Journal Title

      Physical Review B

      Volume: 84 Issue: 9

    • DOI

      10.1103/physrevb.84.094521

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Transmission of Excitations in a Spin-1 Bose Einstein Condensate through a Barrier2011

    • Author(s)
      Watabe S., Kato, Y.
    • Journal Title

      Physical Review A

      Volume: 83 Issue: 5

    • DOI

      10.1103/physreva.83.053624

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Anomalous tunneling of collective excitations and effects of superflow in the polar phase of a spin-1 spinor Bose-Einstein condensate2011

    • Author(s)
      Watabe S., Kato, Y., Ohashi, Y.
    • Journal Title

      Physical Review A

      Volume: 84 Issue: 1

    • DOI

      10.1103/physreva.84.013616

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Transmission of Excitations in a Spin-1 Bose Einstein Condensate through a Barrier2011

    • Author(s)
      S.Watabe, Y.Kato, Y.Ohashi
    • Journal Title

      Physical Review A

      Volume: 83

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Dynamical Density Fluctuations of Superdluids near the Critical Velocity2010

    • Author(s)
      KATO YUSUKE, WATABE SHOHEI
    • Journal Title

      Physical Review Letters

      Volume: Vol.105

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Dynamical Density Fluctuations of Superfluids near the Critical Velocity2010

    • Author(s)
      Y.Kato, S.Watabe
    • Journal Title

      Physical Review Letters

      Volume: 105

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Impurity Scattering Rate in Vortex Core of Sign-reversing s-wave Super conductors2010

    • Author(s)
      Y.Nagai, Y.Kato
    • Journal Title

      Physical Review B

      Volume: 82

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 超流動流安定性の新たな判定法2010

    • Author(s)
      加藤雄介, 渡部昌平
    • Journal Title

      物性研究

      Volume: 95 Pages: 237-269

    • Related Report
      2010 Annual Research Report
  • [Journal Article] Transmission and Reflection of Collective Modes in Spin-1 Bose-Einstein Condensate2010

    • Author(s)
      S.Watabe, Y.Kato
    • Journal Title

      J.Low Temp.Phys. 158

      Pages: 23-28

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Exact Results for Tunneling Problems of Bogoliubov Excitations in the Critical Supercurrent State2010

    • Author(s)
      D.Takahashi, Y.Kato
    • Journal Title

      J.Low.Temp.Phys. 158

      Pages: 65-71

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Criterion for Stability of Superflow Past an Obstacle2010

    • Author(s)
      Y.Kato, S.Watabe
    • Journal Title

      J.Low Temp.Phys. 158

      Pages: 92-98

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] 障害物下の2次元超固体の超流動性2012

    • Author(s)
      穴釜剛、國見昌哉、加藤雄介
    • Organizer
      日本物理学会年会
    • Place of Presentation
      関西学院大学
    • Year and Date
      2012-03-25
    • Related Report
      2011 Final Research Report
  • [Presentation] 超流動固体のBogoliubov励起と超流動性2012

    • Author(s)
      國見昌哉、加藤雄介
    • Organizer
      日本物理学会年会
    • Place of Presentation
      関西学院大学(西宮市、兵庫県)
    • Year and Date
      2012-03-25
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] 障害物下の2次元超固体の超流動性2012

    • Author(s)
      穴釜剛、國見昌哉、加藤雄介
    • Organizer
      日本物理学会年会
    • Place of Presentation
      関西学院大学(西宮市、兵庫県)
    • Year and Date
      2012-03-25
    • Related Report
      2011 Annual Research Report
  • [Presentation] 超流動固体のBogoliubov励起と超流動性2012

    • Author(s)
      國見昌哉、加藤雄介
    • Organizer
      Ultracold Gases : Superfluidity and Strong Correlations (USS-2012)
    • Place of Presentation
      東京理科大学(東京都)
    • Year and Date
      2012-01-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] 障害物下の2次元超固体の超流動性2012

    • Author(s)
      穴釜剛、國見昌哉、加藤雄介
    • Organizer
      Ultracold Gases : Superfluidity and Strong Correlations (USS-2012)
    • Place of Presentation
      東京理科大学(東京都)
    • Year and Date
      2012-01-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] Supersolidity of two-dimensional supersolids in the presence of an obstacle2012

    • Author(s)
      穴釜剛、國見昌哉、加藤雄介
    • Organizer
      ISSP短期研究会量子凝縮系におけるdefectとtopology
    • Place of Presentation
      物性研究所(千葉県)
    • Year and Date
      2012-01-05
    • Related Report
      2011 Annual Research Report
  • [Presentation] 超流動安定性の新たな判定法2011

    • Author(s)
      加藤雄介
    • Organizer
      久保記念シンポジウム
    • Place of Presentation
      学士会館(東京都)(招待講演)
    • Year and Date
      2011-10-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] 異常トンネル効果と南部・ゴールドストーンモード2011

    • Author(s)
      加藤雄介、渡部昌平、大橋洋士
    • Organizer
      日本物理学会秋季大会
    • Place of Presentation
      富山大学(富山県)
    • Year and Date
      2011-09-21
    • Related Report
      2011 Annual Research Report
  • [Presentation] Anomalous Tunneling in BECs and Heibenberg Magnets2011

    • Author(s)
      Kato, Y., Watabe S., Ohashi, Y.
    • Organizer
      Intl.Conf.on Ultra-Low Temp.Phys.(ULT2011)
    • Place of Presentation
      Daejoen,韓国(招待講演)
    • Year and Date
      2011-08-22
    • Related Report
      2011 Annual Research Report
  • [Presentation] Anomalous Tunneling of Spin Wave in Heisenberg Ferromagnet2011

    • Author(s)
      Kato, Y., Watabe S., Ohashi, Y.
    • Organizer
      26th Intl.Conference on Low Temperature Physics (LT26)
    • Place of Presentation
      北京、中国
    • Year and Date
      2011-08-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Anomalous Tunneling of Spin Wave in Polar State of Spin-1 BEC2011

    • Author(s)
      Watabe S., Kato, Y., Ohashi, Y.
    • Organizer
      26th Intl.Conference on Low Temperature Physics (LT26)
    • Place of Presentation
      北京、中国
    • Year and Date
      2011-08-13
    • Related Report
      2011 Annual Research Report
  • [Presentation] Dynamics of One-dimensional Supersolids2011

    • Author(s)
      KUNIMI MASAYA, KOBAYASHI MICHIKAZU, KATO YUSUKE
    • Organizer
      26^<th> Intl. Conf. on Low Temp. Phys.
    • Place of Presentation
      北京(中国)
    • Year and Date
      2011-08-11
    • Related Report
      2011 Final Research Report
  • [Presentation] Dynamics of one-dimensional supersolids2011

    • Author(s)
      Kunimi M., Kobayashi M., Kato Y.
    • Organizer
      26th Intl.Conf.on Low Temperature Physics (LT26)
    • Place of Presentation
      北京、中国
    • Year and Date
      2011-08-11
    • Related Report
      2011 Annual Research Report
  • [Presentation] 1次元固体超流動相のダイナミクスII2011

    • Author(s)
      國見昌哉
    • Organizer
      日本物理学会第66回年次大会
    • Place of Presentation
      新潟大学
    • Year and Date
      2011-03-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dynamics of one-dimensional supersolid2011

    • Author(s)
      Masaya Kunimi
    • Organizer
      UCAM 2011
    • Place of Presentation
      The University of Tokyo
    • Year and Date
      2011-01-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Enhancement and suppression of tunneling of excitations in a spin-1 ferromagnetic BEC2011

    • Author(s)
      Shohei Watabe
    • Organizer
      UCAM2011
    • Place of Presentation
      東京大学
    • Year and Date
      2011-01-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Stability criterion of superfluidity with spectral function of local density2010

    • Author(s)
      Yusuke Kato
    • Organizer
      the 3rd Korea-Japan helium workshop
    • Place of Presentation
      Daejon, Korea
    • Year and Date
      2010-12-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Anomalous Tunneling of Quantum particles in symmetry-broken states2010

    • Author(s)
      Yusuke Kato
    • Organizer
      12^<th> Japanese-American Frontiers of Science Symposium
    • Place of Presentation
      上総アーク、千葉
    • Year and Date
      2010-12-04
    • Related Report
      2010 Annual Research Report
  • [Presentation] 1次元固体超流動相のダイナミクス2010

    • Author(s)
      國見昌哉
    • Organizer
      日本物理学会2010年秋季大会
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2010-09-26
    • Related Report
      2010 Annual Research Report
  • [Presentation] スピン1スピノールBECにおけるスピン波励起の異常トンネル2010

    • Author(s)
      渡部昌平
    • Organizer
      日本物理学会 2010年秋季大会
    • Place of Presentation
      大阪府立大学
    • Year and Date
      2010-09-25
    • Related Report
      2010 Annual Research Report
  • [Presentation] Joseph son effects in one-dimensional super solids2010

    • Author(s)
      KUNIMI MASAYA, NAGAI YUKI, KATO YUSUKE
    • Organizer
      QFS2010
    • Place of Presentation
      グルノーブル(フランス)
    • Year and Date
      2010-08-03
    • Related Report
      2011 Final Research Report
  • [Presentation] Josephson effect in one-dimensional supersolids2010

    • Author(s)
      Yusuke Kato
    • Organizer
      QFS2010
    • Place of Presentation
      Grenoble, France
    • Year and Date
      2010-08-03
    • Related Report
      2010 Annual Research Report
  • [Presentation] Anomalous Tunneling of Spin Wave Excitations in a Spin-1 Spinor Bose-Einstein Condensate2010

    • Author(s)
      Shohei Watabe
    • Organizer
      2nd International Conference on Atomic Physics
    • Place of Presentation
      Cairns, Australia
    • Year and Date
      2010-07-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Josephson effect in one-dimensional supersolids2010

    • Author(s)
      Yusuke Kato
    • Organizer
      Supersolids 2010
    • Place of Presentation
      Paris, France
    • Year and Date
      2010-07-27
    • Related Report
      2010 Annual Research Report
  • [Presentation] Scattering Problems of Low-lying Excitations in Spin-1 Bose-Einstein Condensate2010

    • Author(s)
      Shohei Watabe
    • Organizer
      The International Workshop "Ultracold Fermi Gas : Superfluidity and Strong-Correlation(USS-2010)"
    • Place of Presentation
      東京 日本原子力開発機構 システム計算科学センター
    • Year and Date
      2010-05-14
    • Related Report
      2010 Annual Research Report
  • [Presentation] 1次元超固体のJosephson効果2010

    • Author(s)
      國見昌哉, 永井佑紀, 加藤雄介
    • Organizer
      日本物理学会第65回年次大会
    • Place of Presentation
      岡山大学
    • Year and Date
      2010-03-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] 臨界速度状態近傍におけるBogoliubov励起の透過特性-分岐理論による解析2010

    • Author(s)
      高橋大介, 渡部昌平, 加藤雄介
    • Organizer
      日本物理学会第65回年次大会
    • Place of Presentation
      岡山大学
    • Year and Date
      2010-03-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] 局所スペクトル関数でみる安定な超流動と臨界速度での超流動2010

    • Author(s)
      渡部昌平, 加藤雄介
    • Organizer
      日本物理学会第65回年次大会
    • Place of Presentation
      岡山大学
    • Year and Date
      2010-03-21
    • Related Report
      2009 Annual Research Report
  • [Presentation] Stability Criterion of Superfluidity with Dynamical Density Fluctuations2010

    • Author(s)
      加藤雄介, 渡部昌平
    • Organizer
      International Symposium on Physics of New Quantum Phases in Superclean Materials
    • Place of Presentation
      横浜浜銀ホールViaMare
    • Year and Date
      2010-03-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Superflow of one-dimensional supersolid past an obstacle2010

    • Author(s)
      國見昌哉, 永井佑紀, 加藤雄介
    • Organizer
      International Symposium on Physics of New Quantum Phases in Superclean Materials
    • Place of Presentation
      横浜浜銀ホールViaMare
    • Year and Date
      2010-03-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Tunneling Problems of Excitations in Spin-1 Bose-Einstein Condensate2010

    • Author(s)
      渡部昌平, 加藤雄介
    • Organizer
      International Symposium on Physics of New Quantum Phases in Superclean Materials
    • Place of Presentation
      横浜浜銀ホールViaMare
    • Year and Date
      2010-03-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Transmission properties of Bogoliubov excitations near and at the critical current state2010

    • Author(s)
      高橋大介, 加藤雄介
    • Organizer
      International Symposium on Physics of New Quantum Phases in Superclean Materials
    • Place of Presentation
      横浜浜銀ホールViaMare
    • Year and Date
      2010-03-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] 超流動の安定性に対する新たな判定法2010

    • Author(s)
      加藤雄介
    • Organizer
      特定領域研究「スーパークリーン物質で実現する新しい量子相の物理」A02班研究会
    • Place of Presentation
      八王子セミナーハウス
    • Year and Date
      2010-01-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] 内部自由度を有するボース凝縮体における低エネルギー励起と非磁性不純物の散乱2010

    • Author(s)
      渡部昌平
    • Organizer
      特定領域研究「スーパークリーン物質で実現する新しい量子相の物理」A02班研究会
    • Place of Presentation
      八王子セミナーハウス
    • Year and Date
      2010-01-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] STABILITY OF SUPERFLUID2010

    • Author(s)
      Shohei Watabe
    • Organizer
      International Workshop "Theory of Quantum Gases and Quantum Coherence"
    • Place of Presentation
      Nice, France
    • Related Report
      2010 Annual Research Report
  • [Presentation] 密度スペクトル関数を用いた超流動の安定条件2009

    • Author(s)
      渡部昌平
    • Organizer
      物性科学領域横断研究会 凝縮系科学の最前線
    • Place of Presentation
      東京大学、武田ホール
    • Year and Date
      2009-11-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] 局所的なスペクトル関数による超流動流の安定条件2009

    • Author(s)
      渡部昌平
    • Organizer
      特定領域研究「スーパークリーン物質で実現する新しい量子相の物理」若手秋の学校2009
    • Place of Presentation
      熊本、阿蘇休暇村
    • Year and Date
      2009-09-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] 超流動状態におけるBogoliubov励起の透過反射問題:厳密な結果2009

    • Author(s)
      高橋大介
    • Organizer
      特定領域研究「スーパークリーン物質で実現する新しい量子相の物理」若手秋の学校2009
    • Place of Presentation
      熊本、阿蘇休暇村
    • Year and Date
      2009-09-29
    • Related Report
      2009 Annual Research Report
  • [Presentation] ポテンシャルステップ系における超流動の安定性と局所密度ゆらぎ2009

    • Author(s)
      高橋大介、加藤雄介
    • Organizer
      日本物理学会2009年秋季大会
    • Place of Presentation
      熊本大学
    • Year and Date
      2009-09-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] 局所スペクトル関数による超流動の安定条件2009

    • Author(s)
      渡部昌平、加藤雄介
    • Organizer
      日本物理学会2009年秋季大会
    • Place of Presentation
      熊本大学
    • Year and Date
      2009-09-25
    • Related Report
      2009 Annual Research Report
  • [Presentation] Generalized Criterion for Stability of Superflow Past an Object2009

    • Author(s)
      加藤雄介, 渡部昌平
    • Organizer
      International Symposium on Quantum Fluids and Solids
    • Place of Presentation
      アメリカ、ノースウェスタン大学
    • Year and Date
      2009-08-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Transmission and Reflection of Collective Modes in Spin-1 Bose-Einstein Condensation2009

    • Author(s)
      渡部昌平, 加藤雄介
    • Organizer
      International Symposium on Quantum Fluids and Solids
    • Place of Presentation
      アメリカ、ノースウェスタン大学
    • Year and Date
      2009-08-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] Exact Results for Tunneling Problems of Bogoliubov Excitations in the Critical Supercurrent State2009

    • Author(s)
      高橋大介, 加藤雄介
    • Organizer
      International Symposium on Quantum Fluids and Solids
    • Place of Presentation
      アメリカ、ノースウェスタン大学
    • Year and Date
      2009-08-09
    • Related Report
      2009 Annual Research Report
  • [Presentation] obstacleを通過する超流動の安定性とそのcriterion2009

    • Author(s)
      渡部昌平
    • Organizer
      東京大学グローバルCOE未来を拓く物理科学結集教育拠点 第2回 RA自主研究会
    • Place of Presentation
      山梨県、河口湖
    • Year and Date
      2009-07-01
    • Related Report
      2009 Annual Research Report
  • [Presentation] スピン1ボースアインシュタイン凝縮体における励起のトンネル問題2009

    • Author(s)
      渡部昌平
    • Organizer
      「特定領域研究」スーパークリーン物質で実現する新しい量子相の物理A03,A04班合同研究会
    • Place of Presentation
      箱根、ホテルパウエル
    • Year and Date
      2009-04-28
    • Related Report
      2009 Annual Research Report
  • [Presentation] Stability criterion of superfluidity in the presence of potential barrier2009

    • Author(s)
      加藤雄介
    • Organizer
      「特定領域研究」スーパークリーン物質で実現する新しい量子相の物理A03,A04班合同研究会
    • Place of Presentation
      箱根、ホテルパウエル
    • Year and Date
      2009-04-28
    • Related Report
      2009 Annual Research Report
  • [Book] Dynamics of One-dimensional Quantum Systems : Inverse-square Interaction Models2009

    • Author(s)
      KURAMOTO YOSHIO, KATO YUSUKE
    • Publisher
      Cambrigde Univ. Press
    • Related Report
      2011 Final Research Report
  • [Book] Dynamics of One-dimensional Quantum Systems : Inverse-square Interaction Models2009

    • Author(s)
      Yoshio Kuramoto, Yusuke Kato
    • Total Pages
      486
    • Publisher
      Cambridge Univ.Press
    • Related Report
      2009 Annual Research Report
  • [Remarks]

    • URL

      http://park.itc.u-tokyo.ac.jp/kato-yusuke-lab/

    • Related Report
      2011 Final Research Report
  • [Remarks]

    • URL

      http://park.itc.u-tokyo.ac.jp/kato-yusuke-lab/

    • Related Report
      2011 Annual Research Report
  • [Remarks]

    • URL

      http://park.itc.u-tokyo.ac.jp/kato-yusuke-lab/

    • Related Report
      2010 Annual Research Report
  • [Remarks]

    • URL

      http://park.itc.u-tokyo.ac.jp/kato-yusuke-1ab/

    • Related Report
      2009 Annual Research Report

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Published: 2009-04-01   Modified: 2020-05-15  

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