Semiclassical scar on tori in high dimension
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916617780199424 |
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| author | Yuan, Huanhuan Li, Yong |
| author_facet | Yuan, Huanhuan Li, Yong |
| contents | We show that the eigenfunctions of the self-adjoint elliptic $h-$differential operator $P_{h}(t)$ exhibits semiclassical scar phenomena on the $d-$dimensional torus, under the $σ$-Bruno-Rüssmann condition, instead of the Diophantine one. Its equivalence is described as: for almost all perturbed Hamiltonian's KAM Lagrangian tori $Λ_ω$, there exists a semiclassical measure with positive mass on $Λ_ω$. The premise is that we can obatain a family of quasimodes for the $h-$differential operator $P_{h}(t)$ in the semiclassical limit as $h\rightarrow0$, under the $σ$-Bruno-Rüssmann condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_11445 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semiclassical scar on tori in high dimension Yuan, Huanhuan Li, Yong Mathematical Physics We show that the eigenfunctions of the self-adjoint elliptic $h-$differential operator $P_{h}(t)$ exhibits semiclassical scar phenomena on the $d-$dimensional torus, under the $σ$-Bruno-Rüssmann condition, instead of the Diophantine one. Its equivalence is described as: for almost all perturbed Hamiltonian's KAM Lagrangian tori $Λ_ω$, there exists a semiclassical measure with positive mass on $Λ_ω$. The premise is that we can obatain a family of quasimodes for the $h-$differential operator $P_{h}(t)$ in the semiclassical limit as $h\rightarrow0$, under the $σ$-Bruno-Rüssmann condition. |
| title | Semiclassical scar on tori in high dimension |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2502.11445 |