Ring chains with vertex coupling of a preferred orientation

0540723 - ÚJF 2022 RIV SG eng J - Journal Article
Baradaran, M. - Exner, Pavel - Tater, Miloš
Ring chains with vertex coupling of a preferred orientation.
Reviews in Mathematical Physics. Roč. 33, č. 1 (2021), č. článku 2060005. ISSN 0129-055X. E-ISSN 1793-6659
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : periodic structure * Quantum graphs * spectral gaps
OECD category: Pure mathematics
Impact factor: 1.383, year: 2021
Method of publishing: Limited access
https://doi.org/10.1142/S0129055X20600053

We consider a family of Schrodinger operators supported by a periodic chain of loops connected either tightly or loosely through connecting links of the length l > 0 with the vertex coupling which is non-invariant with respect to the time reversal. The spectral behavior of the model illustrates that the high-energy behavior of such vertices is determined by the vertex parity. The positive spectrum of the tightly connected chain covers the entire halfline while the one of the loose chain is dominated by gaps. In addition, there is a negative spectrum consisting of an infinitely degenerate eigenvalue in the former case, and of one or two absolutely continuous bands in the latter. Furthermore, we discuss the limit l -> 0 and show that while the spectrum converges as a set to that of the tight chain, as it should in view of a result by Berkolaiko, Latushkin, and Sukhtaiev, this limit is rather non-uniform.
Permanent Link: http://hdl.handle.net/11104/0318341