On the asymptotic number of low-lying states in the two-dimensional confined Stark effect

Larry Read

doi:10.1017/fms.2025.10134

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arXiv · 2404.14363

On the asymptotic number of low-lying states in the two-dimensional confined Stark effect

Larry Read

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Abstract

We investigate the Stark operator restricted to a bounded domain $\Omega\subset\mathbb{R}^2$ 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 $\Omega$. 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.

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BibTeX RIS

Larry Read. 2024-04-22. On the asymptotic number of low-lying states in the two-dimensional confined Stark effect. https://doi.org/10.1017/fms.2025.10134

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