Year: 2020
Type: preprint
Abstract: This review paper summarizes the contents of the talk given by the author at the 8th International Congress of Chinese Mathematicians. Using examples of Schrödinger operators on metric graphs, it is shown that a nontrivial topology of the configuration space can give rise to a rich variety of spectral types. In particular, it is shown that the spectrum may be of a pure point type or to have a Cantor structure. We also address the question about the number of open spectral gaps and show that it could be nonzero and finite. Finally, inspired by a recent attempt to model the anomalous Hall effect we analyze a vertex coupling which exhibits high-energy behavior determined by the vertex degree parity.
Source: arXiv (Cornell University)
Author: Exner, Pavel
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3010706052