On the asymptotic number of low-lying states in the two-dimensional confined Stark effect
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917292152979456 |
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| author | Read, Larry |
| author_facet | Read, Larry |
| contents | We investigate the Stark operator restricted to a bounded domain $Ω\subset\mathbb{R}^2$ with Dirichlet boundary conditions. In the semiclassical limit, a three-term asymptotic expansion for its individual eigenvalues has been established, with coefficients dependent on the curvature of $Ω$. We analyse the accumulation of eigenvalues beneath the leading-order terms in these expansions, establishing Weyl-type asymptotics. Furthermore, we derive weak asymptotics for the density of the spectral projector onto these low-lying states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the asymptotic number of low-lying states in the two-dimensional confined Stark effect Read, Larry Spectral Theory Mathematical Physics 35P20 We investigate the Stark operator restricted to a bounded domain $Ω\subset\mathbb{R}^2$ with Dirichlet boundary conditions. In the semiclassical limit, a three-term asymptotic expansion for its individual eigenvalues has been established, with coefficients dependent on the curvature of $Ω$. We analyse the accumulation of eigenvalues beneath the leading-order terms in these expansions, establishing Weyl-type asymptotics. Furthermore, we derive weak asymptotics for the density of the spectral projector onto these low-lying states. |
| title | On the asymptotic number of low-lying states in the two-dimensional confined Stark effect |
| topic | Spectral Theory Mathematical Physics 35P20 |
| url | https://arxiv.org/abs/2404.14363 |