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arXiv · 2007.07865

Spectral asymptotics of all the eigenvalues of Schr\"odinger operators on flat tori

Dario Bambusi·Beatrice Langella·Riccardo Montalto
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Abstract

We study Schr\"odinger operators with Floquet boundary conditions on flat tori obtaining a spectral result giving an asymptotic expansion of all the eigenvalues. The expansion is in $\lambda^{-\delta}$ with $\delta\in(0,1)$ for most of the eigenvalues $\lambda$ (stable eigenvalues), while it is a "directional expansion" for the remaining eigenvalues (unstable eigenvalues). The proof is based on a structure theorem which is a variant of the one proved in \cite{PS10,PS12} and on a new iterative quasimode argument.

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Dario Bambusi, Beatrice Langella, Riccardo Montalto. 2020-07-15. Spectral asymptotics of all the eigenvalues of Schr\"odinger operators on flat tori. https://arxiv.org/abs/2007.07865

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