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arXiv · 2609.02325

A Payne-Weinberger inequality for quantum dot Dirac operators

Joaquim Duran·Albert Mas·Tomás Sanz-Perela
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Abstract

In this work we prove a Payne-Weinberger type inequality for quantum dot Dirac operators defined on bounded and simply connected planar domains. This is a sharp upper bound for their first positive eigenvalue depending only on the isoperimetric deficit of the domain. To this end, we use a recently studied connection with the so-called $\overline\partial$-Robin Laplacian and we establish an analogous inequality for its first eigenvalue, relying on the corresponding inequality for the Robin Laplacian.

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Joaquim Duran, Albert Mas, Tomás Sanz-Perela. 2026-09-02. A Payne-Weinberger inequality for quantum dot Dirac operators. https://arxiv.org/abs/2609.02325

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