2017 Fiscal Year Final Research Report
Semiclassical analysis of spectral and scattering problems associated with energy crossings
| Project/Area Number |
15K17563
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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 |
Basic analysis
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | レゾナンス / エネルギー交差 / 準古典解析 / シュレディンガー方程式 / WKB解 / Effective Hamiltonian / 複素WKB解析 |
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| Outline of Final Research Achievements |
In this project, we have studied the two topics: "Width of resonances for 2x2 Schrodinger operator with energy-level crossings" and "Transition probability for avoided crossings and Stokes geometry".
In the former project, we confirmed that energy-level crossing generates (complex-valued) resonances from (real-valued) embedded eigenvalues and moreover we obtained the precise semi-classical asymptotic expansion of the imaginary part of the resonances.
In the latter, we considered the confluence of turning points, which characterize Stokes geometries. We applied a semi-classical microlocal analysis to this problem, where a complex WKB analysis does not work well. We had spent much time to the control problem of two parameters (confluence and semi-classical), but we succeeded it in the final year.
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| Free Research Field |
解析学基礎
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