Spectral asymptotics of the Laplacian on Platonic solids graphs

0520877 - ÚJF 2020 RIV US eng J - Journal Article
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
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : high-energy eigenvalue asymptotics * quantum graphs * solid grahps
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.317, year: 2019
Method of publishing: Limited access
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.
Permanent Link: http://hdl.handle.net/11104/0305528