2019 Fiscal Year Final Research Report
On the enhancement of tunneling probabilities in multi-dimensional systems
| Project/Area Number |
16K17767
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kyushu Sangyo University (2018-2019)
Tokyo Metropolitan University (2016-2017) |
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Principal Investigator |
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Keywords | 量子カオス / トンネル効果 / 半古典論(WKB法) / 量子化 / ハミルトン力学系 / 非可積分系 / レベルダイナミクス / 幾何学的数値積分法 |
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| Outline of Final Research Achievements |
We studied the enhancement of tunneling probability with dynamical tunneling in multi-dimensional systems and obtained the following results: (1) we constructed an initial wave-packet which approximates the eigenstates of the system by the time-evolution and analyzed the initial condition and the time-evolution based on semiclassical methods. (2) We evaluated the tunneling probabilities by using multi-precision arithmetics and found that tunneling probabilities show a singular dependence on the perturbation strength and Planck constant. (3) We revisited the previous studies on dynamical tunneling and found that our results are out of their assumptions.
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| Free Research Field |
非線形物理
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| Academic Significance and Societal Importance of the Research Achievements |
トンネル効果は物理学のみならず，化学反応，電子工学，量子性が問題となる生命現象などの多岐にわたる分野で生じる．しかしながら，トンネル効果の基礎理論は1次元系のエネルギー障壁トンネル効果のみ想定されている．我々が多次元固有現象である動的トンネル現象の基本的理解を進めたことは，基礎科学においてトンネル効果が顕在化する現象への解明に貢献できるとともに，持続可能な開発を支える，超電導工学や半導体工学などの分野でトンネル効果の制御法といった新しい指導原理の基礎をなすと考えている．
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