Dynamical barriers and quantum effects in Hamiltonian systems

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400405
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: Akira Shudo 首都大学東京, 理工学研究科, 教授 (60206258)
• Co-Investigator(Renkei-kenkyūsha): TANAKA ATUSHI 首都大学東京, 大学院理工学研究科, 助教 (20323264)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 量子カオス / ハミルトン系 / 混合位相空間 / 遅い緩和 / 複素力学系 / 両生固有状態 / 完全WKB解析 / ストークス現象

Outline of Final Research Achievements

We studied classical and quantum dynamics in mixed Hamiltonian systems and obtained the following results: (1) we have rigorously proved the existence of infinity many stability islands for a certain piecewise linear map with hierarchical phase space by introducing a proper symbolic dynamics. (2) we have numerically observed the stable and unstable manifolds for the complex Henon map and found that the orbits are ergodic even though the dynamics in the real plane has mixed phase space, which serves as a semiclassical interpretation for the so-called amphibious eigenfunctions. (3) we have analyzed the Stokes geometry of quantum Henon map satisfying the horseshoe condition based on recent progress of the exact WKB analysis, and found that nontrivial cancellation of saddle points solutions takes places, reflecting the global nature of Stokes geometry.

Free Research Field

非線形物理