Numerical optimisation of Dirac eigenvalues
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00377972" target="_blank" >RIV/68407700:21340/24:00377972 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1088/1751-8121/ad8b01" target="_blank" >https://doi.org/10.1088/1751-8121/ad8b01</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1088/1751-8121/ad8b01" target="_blank" >10.1088/1751-8121/ad8b01</a>
Alternative languages
Result language
angličtina
Original language name
Numerical optimisation of Dirac eigenvalues
Original language description
Motivated by relativistic materials, we develop a numerical scheme to support existing or state new conjectures in the spectral optimisation of eigenvalues of the Dirac operator, subject to infinite-mass boundary conditions. We numerically study the optimality of the regular polygon (respectively, disk) among all polygons of a given number of sides (respectively, arbitrary sets), subject to area or perimeter constraints. We consider the three lowest positive eigenvalues and their ratios. Roughly, we find results analogous to known or expected for the Dirichlet Laplacian, except for the third eigenvalue which does not need to be minimised by the regular polygon (respectively, the disk) for all masses. In addition to the numerical results, a new, mass-dependent upper bound to the lowest eigenvalue in rectangles is proved and its extension to arbitrary quadrilaterals is conjectured.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics
Result continuities
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)
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Physics A: Mathematical and Theoretical
ISSN
1751-8113
e-ISSN
1751-8121
Volume of the periodical
57
Issue of the periodical within the volume
47
Country of publishing house
GB - UNITED KINGDOM
Number of pages
27
Pages from-to
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UT code for WoS article
001349695800001
EID of the result in the Scopus database
2-s2.0-85209359754