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arXiv · 2508.16353

On the asymptotic behavior of the spectral gap for discrete Schr\"odinger operators

Matthias Hofmann·Joachim Kerner·Maximilian Pechmann
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Abstract

In this note we elaborate on the asymptotic behavior of the spectral gap of a class of discrete Schr\"odinger operators defined on a path graph in the limit of infinite volume. We confirm recent results and generalize them to a larger class of potentials using entirely different methods. Notably, we also resolve a conjecture previously proposed in this context. This then yields new insights into the rate at which the spectral gap tends to zero as the volume increases.

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Matthias Hofmann, Joachim Kerner, Maximilian Pechmann. 2025-08-22. On the asymptotic behavior of the spectral gap for discrete Schr\"odinger operators. https://doi.org/10.1177/09217134261465640

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