Spectral asymptotics of the Laplacian on Platonic solids graphs

0520877 - ÚJF 2020 RIV US eng J - Článek v odborném periodiku
Exner, Pavel - Lipovský, J.
Spectral asymptotics of the Laplacian on Platonic solids graphs.
Journal of Mathematical Physics. Roč. 60, č. 12 (2019), č. článku 122101. ISSN 0022-2488. E-ISSN 1089-7658
Grant CEP: GA ČR GA17-01706S
Institucionální podpora: RVO:61389005
Klíčová slova: high-energy eigenvalue asymptotics * quantum graphs * solid grahps
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 1.317, rok: 2019
Způsob publikování: Omezený přístup
https://doi.org/10.1063/1.5116100

We investigate the high-energy eigenvalue asymptotics of quantum graphs consisting of the vertices and edges of the five Platonic solids considering two different types of the vertex coupling. One is the standard delta -condition and the other is the preferred-orientation one introduced in the work by Exner and Tater [Phys. Lett. A 382, 283-287 (2018)]. The aim is to provide another illustration of the fact that the asymptotic properties of the latter coupling are determined by the vertex parity by showing that the octahedron graph differs in this respect from the other four for which the edges at high energies effectively disconnect and the spectrum approaches the one of the Dirichlet Laplacian on an interval.
Trvalý link: http://hdl.handle.net/11104/0305528