Quantum graphs with the Bethe-Sommerfeld property
Autor
Rok
2017
Časopis
Nanosystems - Physics Chemistry Mathematics, 8 (3), 305-309
Web
Obsah
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of graph Hamiltonians, being generic in a sense, inspires the question about the existence of graphs with a finite and nonzero number of spectral gaps. We show that the answer depends on the vertex couplings together with commensurability of the graph edges. A finite and nonzero number of gaps is excluded for graphs with scale invariant couplings; on the other hand, we demonstrate that graphs featuring a finite nonzero number of gaps do exist, illustrating the claim on the example of a rectangular lattice with a suitably tuned delta-coupling at the vertices.
Příklad citace článku:
P. Exner, O. Turek, "Quantum graphs with the Bethe-Sommerfeld property", Nanosystems - Physics Chemistry Mathematics, 8 (3), 305-309 (2017)