High-energy asymptotics of the spectrum of a periodic square lattice quantum graph

0350846 - ÚJF 2011 RIV GB eng J - Článek v odborném periodiku
Exner, Pavel - Turek, Ondřej
High-energy asymptotics of the spectrum of a periodic square lattice quantum graph.
Journal of Physics A-Mathematical and Theoretical. Roč. 43, č. 47 (2010), 474024/1-474024/25. ISSN 1751-8113. E-ISSN 1751-8121
Grant CEP: GA MŠMT LC06002
Výzkumný záměr: CEZ:AV0Z10480505
Klíčová slova: WANNIER-STARK LADDERS * KIRCHHOFFS RULE * SUPERLATTICES
Kód oboru RIV: BE - Teoretická fyzika
Impakt faktor: 1.641, rok: 2010

We investigate a periodic quantum graph in the form of a square lattice with a general self-adjoint coupling at the vertices. We analyse the spectrum's high-energy behaviour. Depending on the coupling type, bands and gaps have different asymptotics. Bands may be flat even if the edges are coupled, and non-flat band widths may behave like O(n(j)), j = 1, 0,-1,-2,-3, as the band index n -> infinity. The gaps may be of asymptotically constant width or linearly growing with the latter case being generic.
Trvalý link: http://hdl.handle.net/11104/0190737