Spectral optimization of Dirac rectangles

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F22%3A00353898" target="_blank" >RIV/68407700:21340/22:00353898 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1063/5.0056278" target="_blank" >https://doi.org/10.1063/5.0056278</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0056278" target="_blank" >10.1063/5.0056278</a>

Result language
angličtina
Original language name
Spectral optimization of Dirac rectangles
Original language description
We are concerned with the dependence of the lowest positive eigenvalue of the Dirac operator on the geometry of rectangles, subject to infinite-mass boundary conditions. We conjecture that the square is a global minimizer under both the area or perimeter constraints. Contrary to the well-known non-relativistic analogs, we show that the present spectral problem does not admit explicit solutions. We prove partial optimization results based on a variational reformulation and newly established lower and upper bounds to the Dirac eigenvalue. We also propose an alternative approach based on symmetries of rectangles and a non-convex minimization problem; this implies a sufficient condition formulated in terms of a symmetry of the minimizer which guarantees the conjectured results.
Czech name
—
Czech description
—

Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX20-17749X" target="_blank" >GX20-17749X: New challenges for spectral theory: geometry, advanced materials and complex fields</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Similar results(10)