Bounds on Eigenfunctions of Quantum Cat Maps
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917603279110144 |
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| author | Kim, Elena Koirala, Robert |
| author_facet | Kim, Elena Koirala, Robert |
| contents | We study $\ell^\infty$ norms of $\ell^2$-normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Bièvre), we show that there exists a sequence of eigenfunctions $u$ with $\|u\|_{\infty}\gtrsim (\log N)^{-1/2}$. For general eigenfunctions we show the upper bound $\|u\|_\infty\lesssim (\log N)^{-1/2}$. Here the semiclassical parameter is $h=(2πN)^{-1}$. Our upper bound is analogous to the one proved by Bérard for compact Riemannian manifolds without conjugate points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_08608 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bounds on Eigenfunctions of Quantum Cat Maps Kim, Elena Koirala, Robert Spectral Theory We study $\ell^\infty$ norms of $\ell^2$-normalized eigenfunctions of quantum cat maps. For maps with short quantum periods (constructed by Bonechi and de Bièvre), we show that there exists a sequence of eigenfunctions $u$ with $\|u\|_{\infty}\gtrsim (\log N)^{-1/2}$. For general eigenfunctions we show the upper bound $\|u\|_\infty\lesssim (\log N)^{-1/2}$. Here the semiclassical parameter is $h=(2πN)^{-1}$. Our upper bound is analogous to the one proved by Bérard for compact Riemannian manifolds without conjugate points. |
| title | Bounds on Eigenfunctions of Quantum Cat Maps |
| topic | Spectral Theory |
| url | https://arxiv.org/abs/2302.08608 |