The fundamental problem of classical dynamics'' in the complexified space and non-integrable tunneling phenomena

2017 Fiscal Year Final Research Report

• Project/Area Number: 15H03701
• 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 立命館大学, 理工学部, 教授 (40151287)
• Co-Investigator(Kenkyū-buntansha): 首藤 啓 首都大学東京, 理工学研究科, 教授 (60206258) ; 高橋 公也 九州工業大学, 大学院情報工学研究院, 教授 (70188001)
• Research Collaborator: YAMADA Hiroaki 山田物理学研究所
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: tunneling effect / semiclassical theory / nonintegrable sysem / quantum chaos / dynamical theory

Outline of Final Research Achievements

First, the transition process from the instanton tunneling, the typical tunneling process in integrable system, to the non-instanton (NI) tunneling process is elucidated by developing a renormalized perturbation method. The remarkable characteristics of the NI tunneling process is clearly explained as an unrenormalizable action of the resonant interaction. Next, the Stokes geometry, which provide rich information for solving an essential difficulty interent in our complexified semiclassical method, is clarified for a quantum map system in the ideally chaotic regime (the so-called horseshoe limit). Finally, a new method for investigating quantum chaotic mixing from 　the auto-correlation characteristics is proposed, and the lifetime in which classical chaotic mixing is maintained in the quantum counterpart is shown to be much longer than the one which has been conjectured so far.

Free Research Field

物理学