非線形・非平衡領域におけるドレスト状態に関する理論的研究

• Project/Area Number: 14077219
• Research Category: Grant-in-Aid for Scientific Research on Priority Areas
• Allocation Type: Single-year Grants
• Review Section: Science and Engineering
• Research Institution: Waseda University
• Principal Investigator: 田崎 秀一 早稲田大学, 理工学術院, 教授 (10260150)
• Project Period (FY): 2002 – 2005
• Project Status: Completed (Fiscal Year 2005)
• Budget Amount: ¥9,400,000 (Direct Cost: ¥9,400,000); Fiscal Year 2005: ¥2,600,000 (Direct Cost: ¥2,600,000); Fiscal Year 2004: ¥2,600,000 (Direct Cost: ¥2,600,000); Fiscal Year 2003: ¥2,600,000 (Direct Cost: ¥2,600,000); Fiscal Year 2002: ¥1,600,000 (Direct Cost: ¥1,600,000)
• Keywords: デコヒーレンス制御 / 射影演算子の方法 / 異常拡散 / 間欠性カオス / C^*代数 / 非平衡定常状態 / 全てのオーダーを超える漸近法 / ハーパー写像 / Decoherence制御 / 量子準位統計 / 間欠性カオス写像 / Frobenius-Perron演算子 / レヴィ拡散 / C*代数 / Gallavotti-Cohenの揺らぎ定理 / 非平衡相転移 / Ion Trap量子演算素子 / 特異連続スペクトル / Mittag-Leffler関数 / 間欠的カオス写像

Research Abstract

主な研究成果は以下の通り。1.有限温度場に起因するドレスト状態の制御:これまでの研究で量子ゼノン効果を用いてデコヒーレンス制御を行う場合、制御振動数が十分大きくないとかえって制御効率が下がることが明らかにされた。他方、量子ゼノン効果を初めて検証した実験では、1回の観測でも状態の時間発展に大きな影響を及ぼすことが示されている。これから、制御対象のダイナミックスの違いにより量子ゼノン制御の効率が変わることが予想される。そこで、2つの素過程が引き続くことで生じる緩和過程(量子ドットの基底状態におけるスピン緩和)についてゼノン制御の効率を調べた。その結果、制御振動数が十分でないとかえって緩和を促進するという一般的傾向が見られるものの、これまで調べた系に比べ悪化の度合いは小さく、制御を達成するのに必要な制御振動数も小さいことが見出された。2.古典カオス系の非平衡状態:カオス研究では非双曲力学系と呼ばれる系の研究が次の重要な課題である。区分的線形な間欠的カオス写像で通常拡散より遅い異常拡散を示す写像について、分布の時間発展を記述するFP演算子のスペクトルと輸送現象の関係を調べ、後者が1に近い第2リーマン面内の固有値に支配されていることを明らかにした。この数学的特徴は量子不安定状態に類似しており、興味深い。3.量子系の非平衡状態:これまで量子1次元導体、L1漸近可換系の非平衡定常状態をC^*代数の方法で調べ、その特徴づけを行ってきた。本研究では、その結果得られた知見を用い、非平衡状態を記述する新たな平均場近似法を構築し、スレイブ・ボソン法と組み合わせて量子複合系の伝導現象を解析した。その結果、線形応答領域では同系の解析で最も信頼されているNRG法の結果を再現し、さらに、非線形応答領域における最新の実験事実を説明することに成功した。

Research Products

• [Journal Article] On the boundary element method for billiards with corners (2005)
  • Author(s): Y.Okada, A.Shudo, S.Tasaki, T.Harayama
  • Journal Title: Journal of Physics A : Math.Gen. 38 Pages: 6675-6688
• [Journal Article] Nonequilibrium Steady States with Bose-Einstein Condensates (2005)
  • Author(s): S.Tasaki, T.Matsui
  • Journal Title: Stochastic Analysis : Classical and Quantum(ed.T.Hida)(World Scientific) Pages: 211-227
• [Journal Article] Long-range spectral statistics of classically integrable systems (2005)
  • Author(s): H.Makino, S.Tasaki
  • Journal Title: Progress of Theoretical Physics 114 Pages: 929-941
• [Journal Article] Nonlinear Transport and Current Fluctuation in an AB Ring with a Quantum Dot (2005)
  • Author(s): J.Takahashi, S.Tasaki
  • Journal Title: Journal of Physical Society of Janan 74, Supplement Pages: 261-264
• [Journal Article] Can one hear the shape of a drum? : revisited (2005)
  • Author(s): Y.Okada, A.Shudo, S.Tasaki, T.Harayama
  • Journal Title: Journal of Physics A : Math.Gen. 38
• [Journal Article] Control of decoherence : analysis and comparison of three different strategies (2005)
  • Author(s): P.Facchi, S.Tasaki, S.Pascazio, H.Nakazato, A.Tokuse, D.Lidar
  • Journal Title: Physical Review A 71
• [Journal Article] Nonlinear Transport and Current Fluctuation in an AB Ring with a Quantum Dot (2005)
  • Author(s): J.Takahashi, S.Tasaki
  • Journal Title: Journal of Physical Society of Japan, Supplement B (印刷中)
• [Journal Article] Control of decoherence: analysis and comparison of three different strategies (2005)
  • Author(s): P.Facchi, S.Tasaki, S.Prascazio, H.Nakazato, A.Tokuse, D.Lidar
  • Journal Title: Physical Review A 71
• [Journal Article] "Can one hear the shape of a drum?":revisited (2005)
  • Author(s): Y.Okada, A.Shudo, S.Tasaki, T.Harayama
  • Journal Title: Journal of Physics A: Math.Gen. 38
• [Journal Article] On Prizoeine's Approaches to Irreversibility - A case study by the baker map - (2004)
  • Author(s): S.Tasaki
  • Journal Title: Discrete Dynamics in Nature and Society 2004:1 Pages: 251-272
• [Journal Article] Control of Decoherence: dynamical decoupling vs quantum Zeno effect (2004)
  • Author(s): S.Tasaki, A.Tokuse, P.Facchi, S.Pascazio
  • Journal Title: International Journal of Quantum Chemistry 98 Pages: 160-172
• [Journal Article] On Entropy Production of A One-dimensional Lattice Conductor (2004)
  • Author(s): S.Tasaki
  • Journal Title: Quantum Information V (eds. T.Hida, K.Saito)
• [Publications] Tasaki, S.: "On Prigogine's Approaches to Irreversibility - A case study by the baker map -"Discrete Dynamics in Nature and Society. (印刷中). (2004)
• [Publications] Tasaki, S.: "On entropy production of a one-dimensional lattice conductor"'Quantum Information V' T.Hida, K.Saito (Eds.). (印刷中). (2004)
• [Publications] Tasaki, S., Tokuse, A., Facchi, P., Pascazio, S.: "Control of Decoherence : dynamical decoupling vs quantum Zeno effect"International Journal of Quantum Chemistry. (印刷中). (2004)
• [Publications] Okada, Y., Shudo, A., Harayama, T., Tasaki, S.: "Can one determine the shape of a quantum billiard table through the eigenenergies and resonances?"Progress of Theoretical Physics. Supplement 150. 397-400 (2003)
• [Publications] Makino, H., Tasaki, S.: "Non-Poissonian Level Spacing of Classically Integrable Quantum Systems Based on the Berry-Robnik Approach"Progress of Theoretical Physics. Supplement 150. 376-380 (2003)
• [Publications] Fuiiyoshi, M., Tasaki, S.: "Friedrichs model with singular continuous spectrum"Journal of Physical Society of Japan. 72, Supp.C. 73-76 (2003)
• [Publications] Makino, H., Tasaki, S: "Derivation from Berry-Robnik distribution caused by spectral accumulation"Journal of Physical Society of Japan. 72,Supp.C. 97-100 (2003)
• [Publications] Tasaki, S., Gaspard, P.: "Spectral characterization of anomalous diffusion of a periodic piecewise linear intermittent map"Physica D. 183. 205-219 (2003)
• [Publications] Makino, H., Tasaki, S.: "Level spacing statistics of classically integrable systems : Investigation along the lines of the Berry-Robnik approach"Physical Review E. 67. 066205 (2003)
• [Publications] Tasaki, S., Matsui, T.: "Fluctuation Theorem, Nonequilibrium Steady States and MacLennan-Zubarev Ensembles of a Class of Large Quantum Systems"'Fundamental Aspects of Quantum Physics' L.Accardi, S.Tasaki (Eds.). 100-119 (2003)
• [Publications] Accardi, L., Tasaki, S.(eds.): "Fundamental Aspects of Quantum Physics"World Scientific, Singapore. 340 (2003)
• [Publications] Tasaki, S., Matsui, T.: "Fluctuation Theorem, Nonequilibrium Steady States and MacLennan-Zubarev Ensembles of a Class of Large Quantum Systems"In 'Fundamental Aspects of Quantum Physics' L.Accardi, S.Tasaki (Eds.). (印刷中). (2003)
• [Publications] Honda, H., Ogura H., Tasaki, S., Chiba A.: "Two-phase coexisting state of n-hexatriacontane in the first-order phase transition"Thermochimica Acta. (印刷中). (2003)
• [Publications] Tasaki, S.: "On entropy production of a one-dimensional lattice conductor"In 'Quantum Information V'T.Hida, K.Saito (Eds.). (印刷中). (2003)
• [Publications] Tasaki S.: "Thermodynamic Behaviors of Large Dynamical System -quantum 1d conductor and classical multibaker map -"in "Dynamics of Dissipation", P.Garbaczewski, R.Olkiewicz (Eds.), Lecture Notes in Physics 597. 395-412 (2002)
• [Publications] Tasaki S., Gaspard P.: "Spectral Properties of a Piecewise Linear Intermittent Map"Journal of Statistical Physics. 109(3). 803-820 (2002)
• [Publications] Tasaki S.: "Irreversibility in reversible multibaker maps"Advances in Chemical Physics. 122. 70-107 (2002)