Multi-dimensional tunnelling and chaos in complexified phase space

• Project/Area Number: 20340100
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Ritsumeikan University
• Principal Investigator: IKEDA Kensuke Ritsumeikan University, 理工学部, 教授 (40151287)
• Co-Investigator(Kenkyū-buntansha): TAKAHASHI Kin'Ya 九州工業大学, 情報工学部, 准教授 (70188001) ; SHUDO Akira 首都大学東京, 大学院・理工学研究科, 教授 (60206258) ; ISHII Yutaka 九州大学, 大学院・ 数理学研究院, 准教授 (20304727)
• Research Collaborator: HYOUGUCHI Tadanori 立命館大学, 総合理工学研究機構, リサーチアシスタント
• Project Period (FY): 2008 – 2010
• Project Status: Completed (Fiscal Year 2010)
• Budget Amount: ¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000); Fiscal Year 2010: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2009: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2008: ¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
• Keywords: 非平衡・非線形物理学 / カオス / トンネル効果 / 半古典理論 / 複素力学系理論

Research Abstract

There are no orbits in quantum world. It reveals that the tunnelling phenomena, a most wanderful quantum phenomenon, can be completely understood in terms of the orbits which are running in the "complexified space",even when the system exhibits very complex chaos motion.

Research Products

• [Journal Article] Structural change of the tunneling spectrum with perturbation frequency (2010)
  • Author(s): 高橋公也,池田研介
  • Journal Title: J.Phys.A 43巻 Pages: 192001-192010
  • Peer Reviewed
• [Journal Article] Dynamical tunneling in many-dimensional chaotic systems (2010)
  • Author(s): 石川明幸,田中篤司,首藤啓
  • Journal Title: Physical Review Letters 104巻
  • Peer Reviewed
• [Journal Article] Structural change of the tunneling spectrum with perturbation frequency (2010)
  • Author(s): 高橋公也、池田研介
  • Journal Title: Journal of Physics A Volume: 43巻 Pages: 192001-192001
  • Peer Reviewed
• [Journal Article] Recovery of chaotic tunneling due to destruction of dynamical localization by an external noise (2009)
  • Author(s): 石川明幸,田中篤司,首藤啓
  • Journal Title: Physical Review E 80巻
  • Peer Reviewed
• [Journal Article] Julia set and chaotic tunnelling I (2009)
  • Author(s): 首藤啓,石井豊,池田研介
  • Journal Title: J.Phys.A 42巻
  • Peer Reviewed
• [Journal Article] Spectroscopic signature of the transition in a tunnaling mechanism from the instanton path to a complexified stable-unstable manifolds. (2009)
  • Author(s): 高橋公也,池田研介
  • Journal Title: Phys.Rev.A 79巻
  • Peer Reviewed
• [Journal Article] Overlooked Branch Cut in Steepest Descent Method-Switching Line and Atomic Domain- (2009)
  • Author(s): 俵口忠功,瀬戸亮平,足立聡
  • Journal Title: Prog.Theor.Phys. 122巻 Pages: 1311-1346
  • NAID: 110007502692
  • Peer Reviewed
• [Journal Article] Overlooked Degree of Freedom in Steepest Descent Method-Steepest Descent Method Corresponding to Divergence-Free WKB Method- (2009)
  • Author(s): 俵口忠功,瀬戸亮平,足立聡
  • Journal Title: Prog.Theor.Phys. 122巻 Pages: 1347-1376
  • NAID: 110007502693
  • Peer Reviewed
• [Journal Article] Julia set and chaotic tunnelling I (2009)
  • Author(s): 首藤啓、石井豊、池田研介
  • Journal Title: Journal of Physics A 42
  • Peer Reviewed
• [Journal Article] Julia set and chaotic tunnelling II (2009)
  • Author(s): 首藤啓、石井豊、池田研介
  • Journal Title: Journal of Physics A 42
  • Peer Reviewed
• [Journal Article] Spectroscopic signature of the transition in tunnelling mechamism from instanton path to complexied stable-unstable manifold (2009)
  • Author(s): 高橋公也, 池田研介
  • Journal Title: Physical Review A (印刷中)
  • Peer Reviewed
• [Journal Article] Chaos attracts tunneling trajectories : aniversal mechanism ofchaotic tunneling (2008)
  • Author(s): 首藤啓,石井豊,池田研介
  • Journal Title: Euro.Phys.Letter 81巻 Pages: 50003-50007
  • Peer Reviewed
• [Journal Article] Stokes geometry for the quantum H' enon map (2008)
  • Author(s): 首藤啓,池田研介
  • Journal Title: Nonlinearity 21巻 Pages: 1831-1880
  • Peer Reviewed
• [Journal Article] A plateau structure in the tunnelling spectrum as a manifestation of a new tunnelling mechanism in multi-dimensional barrier systems (2008)
  • Author(s): 高橋公也,池田研介
  • Journal Title: J.Phys.A 41巻 Pages: 95101-95135
  • Peer Reviewed
• [Journal Article] A plateau structure in the tunnelling spectrum as a manifestation of a new tunnelling mechanism in multi-dimen sional barrier systems (2008)
  • Author(s): 高橋公也, 池田研介
  • Journal Title: Journal of Physics A 41巻 Pages: 95101-95135
  • Peer Reviewed
• [Journal Article] Structual change of tunneling spectrum with perturbation frequency
  • Author(s): 高橋公也、池田研介
  • Journal Title: Journal of Physics A (印刷中(掲載決定))
  • Peer Reviewed
• [Journal Article] Overlooked branch cut in steepest descent method-switching line and atomic domain-
  • Author(s): 俵口忠功、足立聡
  • Journal Title: Progress of theoretical physics (印刷中(掲載決定))
  • NAID: 110007502692
  • Peer Reviewed
• [Book] Dynamical Tunneling : Theory and Experiment7章(P.Schlagheck and S.Keshavamurthy 編) (2011)
  • Author(s): 首藤啓,池田研介
  • Publisher: CRC Press
• [Book] Dynamical Tunneling : Theory and Experiment5章(P.Schlagheck and S.Keshavamurthy 編) (2011)
  • Author(s): 高橋公也
  • Publisher: CRC Press
• [Book] Dynamical Tunneling : Theory and Experiment(S.Keshavamurthy, P.Schlagheck編) 5章 Semiclassical Analysis of Multidimensional Barrier Tunneling (2011)
  • Author(s): 高橋公也
  • Publisher: CRC Press
• [Book] Dynamical Tunneling : Theory and Experiment(S.Keshavamurthy, P.Schlagheck編)7章 Complex Semiclassical Approach to Chaotic Tunneling (2011)
  • Author(s): 首藤啓、池田研介
  • Publisher: CRC Press