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熱場の理論による補足ポテンシャル中の中性原子気体の非平衡状態の研究

Research Project

Project/Area Number 17740258
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionJapan Atomic Energy Agency (2007)
Waseda University (2005-2006)

Principal Investigator

奥村 雅彦  Japan Atomic Energy Agency, システム計算科学センター, 特定課題推進員 (20386600)

Project Period (FY) 2005 – 2007
Project Status Completed (Fiscal Year 2007)
Budget Amount *help
¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2007: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2006: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2005: ¥400,000 (Direct Cost: ¥400,000)
Keywords場の量子論 / 物性基礎論 / 数理物理 / 非平衡・非線形物理学
Research Abstract

[研究目的] 本研究の目的は中性原子気体系における非平衡現象を量子場の理論の枠組みで記述して実験との比較を試み、量子多体系における非平衡現象の理解を進めることである。今年度は特に(1)前年度までに得られていた量子Boltzmann方程式の拡張、(2)動的不安定性の量子場の理論による定式化を具体的目標に挙げた。
[研究方法] (1)解析的に方程式を求め、数値計算により系の時間発展を追う。(2)準粒子描像を仮定し、線形応答によって不安定性を定量的に記述する。 また、安定なパラメータを基準とした摂動計算により、解析的に安定性条件を求めた。
[研究結果] (1)については1次元系について予備の数値計算を行ったが、次元の特殊性のためか、思うように緩和しなかったため、現在次元を上げた計算に向けてプログラムを改良中である。次に、(2)については不安定状態の初期の線形挙動を量子場の理論の枠内で記述するために新たな量子状態を構成し、その定式化に至った。その応用として、光学格子中の流れのあるボース凝縮体の解析を行い、量子揺らぎの入らないシミュレーションと無矛盾な結果を得たうえに、有意な量子効果を見ることができた。また、凝縮体が高次量子渦を持つ場合、2モード近似を用いて相互作用定数が小さい時に限り、解析的に高次量子渦が不安定になる条件を求め、すべての高次量子渦が不安定であることを示した。また、この2モードのみを考慮すれば不安定性の議論に十分であることも示した。

Report

(3 results)
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • 2005 Annual Research Report
  • Research Products

    (21 results)

All 2008 2007 Other

All Journal Article (13 results) (of which Peer Reviewed: 6 results) Presentation (8 results)

  • [Journal Article] Quantum field theoretical analysis on unstable behavior of Bose-Einstein condenstates in optical lattices2008

    • Author(s)
      K. Kobayashi, M. Mine, M. Okumura, and Y. Yamanaka
    • Journal Title

      Annals of Physics 323

      Pages: 12471270-12471270

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Condition for Emergence of Complex Eigenvalues in the Bogoliubov-de Gennes Equations2008

    • Author(s)
      Y. Nakamura, M. Mine, M. Okumura, and Y. Yamanaka
    • Journal Title

      Physical Review A 77

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Condition for the existence of complex modes in a trapped Bose-Einstein condensate with a highly quantized vortex2007

    • Author(s)
      E. Fukuyama, M. Mine, T. Sunaga, M. Okumura, and Y. Yamanaka
    • Journal Title

      Physical Review A 76

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum field theoretical description of unstable behavior of trapped Bose-Einstein condensates with complex eigenvalues of Bogoliubov-de Gennes equations2007

    • Author(s)
      M. Mine, M. Okumura, T. Sunaga, and Y. Yamanaka
    • Journal Title

      Annals of Physics 322

      Pages: 23272349-23272349

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum Field Theoretical Description of Dynamical Instability of Trapped Bose-Einstein Condensates2007

    • Author(s)
      M. Mine, M. Okumura, T. Sunaga, and Y. Yamanaka
    • Journal Title

      Journal of Low Temperature Physics 148

      Pages: 331336-331336

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Condition for Existence of Complex Modes in Trapped Bose-Einstein Condensate with a Highly Quantized Vortex2007

    • Author(s)
      T. Sunaga, E. Fukuyama, M. Mine, M. Okumura and Y. Yamanaka
    • Journal Title

      Journal of Low Temperature Physics 148

      Pages: 381386-381386

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantum Field Theoretical Description of Unstable Behavior of a Bose-Einstein Condensate with a Highly Quantized Vortex in a Harmonic Potential2007

    • Author(s)
      M.Okumura, M.Mine, T.Sunaga, Y.Yamanaka
    • Journal Title

      Laser Physics Vol.17,No.2

      Pages: 211-214

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Condensates in a Trapping Potential with Complex Eigenvalues of Bogoliubov-de Gennes Equations

    • Author(s)
      M.Mine, M.Okumura, T.Sunaga, Y.Yamanaka
    • Journal Title

      Annals of Physics. (Accepted for publication)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Condensates in a Trapped Potential with Complex Eigenvalues of Bogoliubov-de Gennes Equations

    • Author(s)
      M.Mine, M.Okumura, T.Sunaga, Y.Yamanaka
    • Journal Title

      Journal of Low Temperature Physics. (Accepted for publication)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The Condition for Existence of Complex Modes in Trapped Bose-Einstein Condensates with a Highly Quantized Vortex

    • Author(s)
      T.Sunaga, E.Fukuyama, M.Mine, M.Okumura, Y.Yamanaka
    • Journal Title

      Journal of Low Temperature Physics. (Accepted for publication)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Unitarily Inequivalent Vacua in Bose-Einstein Condensation of Trapped Gases

    • Author(s)
      M.Okumura, Y.Yamanaka
    • Journal Title

      Physica A (Accepted for publication)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Goldstone Theorem, Hugenholtz-Pines Theorem and Ward-Takahashi Relation in Finite Volume Bose-Einstein Condensed Gases

    • Author(s)
      H.Enomoto, M.Okumura, Y.Yamanaka
    • Journal Title

      Annals of Physics (Accepted for publication)

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Effect of Zero-Mode on the Response of Trapped Bose-Condensates

    • Author(s)
      M.Mine, T.Koide, M.Okumura, Y.Yamanaka
    • Journal Title

      Progress of Theoretical Physics (Accepted for publication)

    • Related Report
      2005 Annual Research Report
  • [Presentation] Condition for the existence of complex modes in a trapped Bose-Einstein condensate with a highly quantized vortex2008

    • Author(s)
      M. Mine, E. Fukuyama, T. Sunaga, M. Okumura, and Y. Yamanaka
    • Organizer
      APS March Meeting 2008
    • Place of Presentation
      New Orleans, USA
    • Year and Date
      2008-03-11
    • Related Report
      2007 Annual Research Report
  • [Presentation] Quantum Field Theoretical Description of Dynamical instability of Trapped Bose-Einstein Condensates2008

    • Author(s)
      M. Mine, M. Okumura, T. Sunaga, and Y. Yamanaka
    • Organizer
      Ultracold NanoMatter 2008
    • Place of Presentation
      Toronto, Canada
    • Year and Date
      2008-02-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] On the Condition of the Emergence of Complex Eigenvalues in the BdG Equation2008

    • Author(s)
      Y. Nakamura, M. Mine, M. Okumura, and Y. Yamanaka
    • Organizer
      Ultracold NanoMatter 2008
    • Place of Presentation
      Toronto, Canada
    • Year and Date
      2008-02-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] Unstable Behavior of a BEC in an Optical Lattice-Quantum Theoretical Approach2008

    • Author(s)
      K. Kobayashi, M. Mine, M. Okumura, and Y. Yamanaka
    • Organizer
      Ultracold NanoMatter 2008
    • Place of Presentation
      Toronto, Canada
    • Year and Date
      2008-02-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] 光学格子中Bose-Einstein凝縮における動的不安定性の場の理論的解析2007

    • Author(s)
      小林恵太, 峰真如, 奥村雅彦, 山中由也
    • Organizer
      日本物理学会第62回年次大会
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-09-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Bogoliubov-de Gennes方程式における複素固有値出現条件の解析2007

    • Author(s)
      中村祐介, 峰真如, 奥村雅彦, 山中由也
    • Organizer
      日本物理学会第62回年次大会
    • Place of Presentation
      北海道大学
    • Year and Date
      2007-09-21
    • Related Report
      2007 Annual Research Report
  • [Presentation] Analytic Expression of the Condition for the Existence of Complex Modes for a Trapped Bose-Einstein Condensate with a Highly Quantized Vortex2007

    • Author(s)
      T. Sunaga, E. Fukuyama, M. Mine, M. Okumura, and Y. Yamanaka
    • Organizer
      The 5th 21st century COE symposium on Physics of Selforganization Systems
    • Place of Presentation
      早稲田大学
    • Year and Date
      2007-09-14
    • Related Report
      2007 Annual Research Report
  • [Presentation] Complex Eigenvalues Associated with Trapped BEC and Field Theoretical Description of Unstable Behavior2007

    • Author(s)
      M. Mine, M. Okumura, T. Sunaga, and Y. Yamanaka
    • Organizer
      QuAMP 2007
    • Place of Presentation
      London, UK
    • Year and Date
      2007-09-12
    • Related Report
      2007 Annual Research Report

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Published: 2005-04-01   Modified: 2016-04-21  

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