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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.15992 |
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| _version_ | 1866914449606049792 |
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| author | Wang, Weiwei Wu, Xianchao |
| author_facet | Wang, Weiwei Wu, Xianchao |
| contents | This paper investigates the upper bound of the integral of $L^2$-normalized joint eigenfunctions over geodesics in a two-dimensional quantum completely integrable system. For admissible geodesics, we rigorously establish an asymptotic decay rate of $O(h^{1/2})$. This represents a polynomial improvement over the previously well known $O(1)$ bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_15992 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Average estimate for Eigenfunctions along geodesics in the quantum completely integrable case Wang, Weiwei Wu, Xianchao Analysis of PDEs This paper investigates the upper bound of the integral of $L^2$-normalized joint eigenfunctions over geodesics in a two-dimensional quantum completely integrable system. For admissible geodesics, we rigorously establish an asymptotic decay rate of $O(h^{1/2})$. This represents a polynomial improvement over the previously well known $O(1)$ bound. |
| title | Average estimate for Eigenfunctions along geodesics in the quantum completely integrable case |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2506.15992 |