Upper bounds on eigenvalue spacing for decaying potentials
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911405471432704 |
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| author | Lukic, Milivoje Simanek, Brian |
| author_facet | Lukic, Milivoje Simanek, Brian |
| contents | We study decaying half-line Schrödinger operators and the local eigenvalue spacing of their Dirichlet restrictions. While absolutely continuous spectrum is strongly associated with bulk universality and clock behavior, singular spectral measures can correspond to varied local behaviors. In this work, the rate of decay of the potential is shown to give upper bounds for the spacing of Dirichlet eigenvalues on finite intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21108 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Upper bounds on eigenvalue spacing for decaying potentials Lukic, Milivoje Simanek, Brian Spectral Theory Classical Analysis and ODEs We study decaying half-line Schrödinger operators and the local eigenvalue spacing of their Dirichlet restrictions. While absolutely continuous spectrum is strongly associated with bulk universality and clock behavior, singular spectral measures can correspond to varied local behaviors. In this work, the rate of decay of the potential is shown to give upper bounds for the spacing of Dirichlet eigenvalues on finite intervals. |
| title | Upper bounds on eigenvalue spacing for decaying potentials |
| topic | Spectral Theory Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2601.21108 |