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Eigenvalue bounds for quantum dot Dirac operators
Abstract
We exploit the connection between quantum dot Dirac operators and ∂̅-Robin Laplacians. First, we find a graphical relation between their smallest positive eigenvalues, which allows us to deduce a recipe for translating bounds (from above and below) from one to the other. As an application, we provide new upper and lower bounds for the eigenvalues of the quantum dot Dirac operators, which depend only on geometric quantities of the underlying domain. In particular, we obtain some Faber-Krahn type inequalities for convex thin domains.
Versions
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BibTeX
@misc{duran2026eigenvalue,
title = {{Eigenvalue bounds for quantum dot Dirac operators}},
author = {Joaquim Duran},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.30228},
eprint = {2605.30228},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30228},
}
RIS
TY - UNPB
TI - Eigenvalue bounds for quantum dot Dirac operators
AU - Joaquim Duran
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2605.30228
UR - https://arxiv.org/abs/2605.30228
AB - We exploit the connection between quantum dot Dirac operators and ∂̅-Robin Laplacians. First, we find a graphical relation between their smallest positive eigenvalues, which allows us to deduce a recipe for translating bounds (from above and below) from one to the other. As an application, we provide new upper and lower bounds for the eigenvalues of the quantum dot Dirac operators, which depend only on geometric quantities of the underlying domain. In particular, we obtain some Faber-Krahn type inequalities for convex thin domains.
ER -