1. Gaps in the Spectrum of a Cuboidal Periodic Lattice Graph.
- Author
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Turek, Ondřej
- Subjects
- *
QUANTUM graph theory , *LATTICE theory , *COEFFICIENTS (Statistics) , *GRAPHIC methods , *IRRATIONAL numbers - Abstract
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with δ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As the main result, we find a connection between the arrangement of the gaps and the coefficients in a continued fraction associated with the ratio of edge lengths of the lattice. This knowledge enables a straightforward construction of a periodic quantum graph with any required number of spectral gaps and—to some degree—to control their positions; i.e. to partially solve the inverse spectral problem. [ABSTRACT FROM AUTHOR]
- Published
- 2019
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