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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 ∂̅-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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Cite

BibTeXRIS
BibTeX
@misc{duran2026payneweinberger,
  title = {{A Payne-Weinberger inequality for quantum dot Dirac operators}},
  author = {Joaquim Duran and Albert Mas and Tomás Sanz-Perela},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02325},
  eprint = {2609.02325},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02325},
}
RIS
TY  - UNPB
TI  - A Payne-Weinberger inequality for quantum dot Dirac operators
AU  - Joaquim Duran
AU  - Albert Mas
AU  - Tomás Sanz-Perela
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02325
UR  - https://arxiv.org/abs/2609.02325
AB  - 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 ∂̅-Robin Laplacian and we establish an analogous inequality for its first eigenvalue, relying on the corresponding inequality for the Robin Laplacian.
ER  -