A Sharp Upper Bound on the Spectral Gap for Graphene Quantum Dots

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F19%3A00504281" target="_blank" >RIV/61389005:_____/19:00504281 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s11040-019-9310-z" target="_blank" >https://doi.org/10.1007/s11040-019-9310-z</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11040-019-9310-z" target="_blank" >10.1007/s11040-019-9310-z</a>

Result language
angličtina
Original language name
A Sharp Upper Bound on the Spectral Gap for Graphene Quantum Dots
Original language description
The main result of this paper is a sharp upper bound on the first positive eigenvalue of Dirac operators in two dimensional simply connected C-3-domains with infinite mass boundary conditions. This bound is given in terms of a conformal variation, explicit geometric quantities and of the first eigenvalue for the disk. Its proof relies on the min-max principle applied to the squares of these Dirac operators. A suitable test function is constructed by means of a conformal map. This general upper bound involves the norm of the derivative of the underlying conformal map in the Hardy space H-2(D). Then, we apply known estimates of this norm for convex and for nearly circular, star-shaped domains in order to get explicit geometric upper bounds on the eigenvalue. These bounds can be re-interpreted as reverse Faber-Krahn-type inequalities under adequate geometric constraints.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project
<a href="/en/project/GA17-01706S" target="_blank" >GA17-01706S: Mathematical-Physics Models of Novel Materials</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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