2023 Fiscal Year Annual Research Report
Resurgent theory in quantum mechanics and its applications
| Project/Area Number |
22KF0323
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| Allocation Type | Multi-year Fund |
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
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) |
2023-03-08 – 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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