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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.02092 |
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| _version_ | 1866910101293498368 |
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| author | Drouot, Alexis Lyman, Curtiss |
| author_facet | Drouot, Alexis Lyman, Curtiss |
| contents | In this paper, we develop a systematic framework to study the dispersion surfaces of Schr{ö}dinger operators $ -Δ+ V$, where the potential $V \in C^\infty(\mathbb{R}^n,\mathbb{R})$ is periodic with respect to a lattice $Λ\subset \mathbb{R}^n$ and respects the symmetries of $Λ$. Our analysis combines the theory of holomorphic families of operators of type (A) with the seminal work of Fefferman--Weinstein \cite{feffer12}. It allows us to extend results on the existence of spectral degeneracies past a perturbative regime. As an application, we describe the generic structure of some singularities in the band spectrum of Schrödinger operators invariant under the three-dimensional simple, body-centered and face-centered cubic lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02092 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Band spectrum singularities for Schrödinger operators Drouot, Alexis Lyman, Curtiss Mathematical Physics In this paper, we develop a systematic framework to study the dispersion surfaces of Schr{ö}dinger operators $ -Δ+ V$, where the potential $V \in C^\infty(\mathbb{R}^n,\mathbb{R})$ is periodic with respect to a lattice $Λ\subset \mathbb{R}^n$ and respects the symmetries of $Λ$. Our analysis combines the theory of holomorphic families of operators of type (A) with the seminal work of Fefferman--Weinstein \cite{feffer12}. It allows us to extend results on the existence of spectral degeneracies past a perturbative regime. As an application, we describe the generic structure of some singularities in the band spectrum of Schrödinger operators invariant under the three-dimensional simple, body-centered and face-centered cubic lattices. |
| title | Band spectrum singularities for Schrödinger operators |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2410.02092 |