2022 Fiscal Year Annual Research Report
Resurgent theory in quantum mechanics and its application
| Project/Area Number |
21F21020
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| Allocation Type | Single-year Grants |
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| Research Institution | Tokyo Metropolitan University |
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| Foreign Research Fellow |
ネメシュ ゲルグ 東京都立大学, 理学研究科, 特任准教授 (20994495)
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| Project Period (FY) |
2021-11-18 – 2024-03-31
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| Keywords | asymptotics / resurgence / exact WKB analysis / Borel summability |
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| Outline of Annual Research Achievements |
We have established the Borel summability of formal solutions for a broad class of higher-order linear ODEs with a large parameter. The problem of Borel summability for formal solutions of such equations has posed a longstanding challenge in the field of exact asymptotics. A manuscript summarising these results is currently under review. Furthermore, we investigated the resurgence properties of the incomplete gamma function in the transition region by analysing the asymptotics of the late coefficients in its asymptotic expansion. The findings have been published in the journal SIGMA. Prior to this paper, there has been no investigation in the existing literature regarding the resurgence properties of asymptotic expansions in transition regions.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The research progressed smoothly. We have demonstrated the Borel summability of formal solutions for a wide range of higher-order linear ODEs with a large parameter. The issue of Borel summability for formal solutions of these equations has been a longstanding challenge in the field of exact asymptotics.
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| Strategy for Future Research Activity |
We aim to establish Borel summability for a broader class of equations where the characteristic equation is not a simple monomial. Additionally, we seek to derive connection formulas across Stokes lines.
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