Work

A Payne-Weinberger inequality for quantum dot Dirac operators

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.02325

Authors: Duran, Joaquim, Mas, Albert, Sanz-Perela, Tomás

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Centres de Recerca de Catalunya, Generalitat de Catalunya, Agencia Estatal de Investigación

Awards: G128764640, G3480869486, G3693695517, G4228227490, G5080475149, G6325762137, G7084143925, G7476827183, G84477964

OpenAlex ID: W7207762744

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