Spectrum of a Dilated Honeycomb Network

0443407 - ÚJF 2016 RIV CH eng J - Článek v odborném periodiku
Exner, Pavel - Turek, Ondřej
Spectrum of a Dilated Honeycomb Network.
Integral Equations and Operator Theory. Roč. 81, č. 4 (2015), s. 535-557. ISSN 0378-620X. E-ISSN 1420-8989
Grant CEP: GA ČR(CZ) GA14-06818S
Institucionální podpora: RVO:61389005
Klíčová slova: quantum graphs * Hexagon lattice * Laplace operator * Vertex delta-coupling * spectrum
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 0.956, rok: 2015

We analyze spectrum of Laplacian supported by a periodic honeycomb lattice with generally unequal edge lengths and a delta type coupling in the vertices. Such a quantum graph has nonempty point spectrum with compactly supported eigenfunctions provided all the edge lengths are commensurate. We derive conditions determining the continuous spectral component and show that existence of gaps may depend on number-theoretic properties of edge lengths ratios. The case when two of the three lengths coincide is discussed in detail.
Trvalý link: http://hdl.handle.net/11104/0246141