Reconnection of Unstable/Stable Manifolds of the Harper Map : Asymptotics-Beyond-All-Orders Approach(Condensed Matter and Statistical Physics)

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概要

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• The Harper map is one of the simplest chaotic systems exhibiting reconnection of invariant manifolds. The method of asymptotics beyond all orders (ABAO) is used to construct unstable/stable manifolds of the Harper map. By enlarging the neighborhood of a singularity, the perturbative solution of the unstable manifold is expressed as a Borel summable asymptotic expansion in a sector including t=-∞ and is analytically continued to the other sectors, where the solution acquires new terms describing heteroclinic tangles. It is shown that when the parameter is changed, upon reaching the reconnection threshold, the unstable/stable manifolds acquire new oscillatory parts corresponding to the heteroclinic tangle after the reconnection.

• 理論物理学刊行会の論文
• 2006-10-25

著者

• Tasaki Shuichi

  Advanced Institute For Complex Systems And Department Of Applied Physics School Of Science And Engin

• Ajisaka Shigeru

  Waseda Univ. Tokyo Jpn

• Ajisaka Shigeru

  Advanced Institute For Complex Systems And Department Of Applied Physics School Of Science And Engin

• Ajisaka Shigeru

  Depto. De Fisica Facultad De Ciencias Fisicas Y Matematicas Universidad De Chile

• TASAKI Shuichi

  Advanced Institute for Complex Systems and Department of Applied Physics, School of Science and Engineerings, Waseda University

• AJISAKA Shigeru

  Advanced Institute for Complex Systems and Department of Applied Physics, School of Science and Engineerings, Waseda University

関連論文

• Nonequilibrium Peierls Transition(Condensed Matter Physics)
• Reconnection of Stable/Unstable Manifolds of the Harper Map(6) Approaches from mathematical science and quantum information, Chaos and Nonlinear Dynamics in Quantum-Mechanical and Macroscopic Systems)
• Reconnection of Unstable/Stable Manifolds of the Harper Map : Asymptotics-Beyond-All-Orders Approach(Condensed Matter and Statistical Physics)
• Nonequilibrium Steady States and MacLennan-Zubarev Ensembles in a Quantum Junction System(Physics of Non-Equilibrium Systems: Self-Organized Structures and Dynamics Far from Equilibrium)
• Quantum statistical mechanics in infinitely extended systems : C^* algebraic approach(Perspectives of Nonequilibrium Statistical Physics-The Memory of Professor Shuichi Tasaki-)

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