Abstract
Let Γ be an arbitrary periodic metric graph, which does not coincide with a line. We consider the Hamiltonian on its edges; here ϵ > 0 is a small parameter. Let. We show that under a proper choice of vertex conditions the spectrum has at least m gaps as ϵ is small enough. We demonstrate that the asymptotic behavior of these gaps and the asymptotic behavior of the bottom of as ϵ → 0 can be completely controlled through a suitable choice of coupling constants standing in those vertex conditions. We also show how to ensure for fixed (small enough) ϵ the precise coincidence of the left endpoints of the first m spectral gaps with predefined numbers.
Original language | English |
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Article number | 405202 |
Journal | Journal of Physics A: Mathematical and Theoretical |
Volume | 53 |
Issue number | 40 |
DOIs | |
Publication status | Published - 9 Oct 2020 |
Keywords
- Control of spectrum
- Periodic quantum graphs
- Spectral gaps
- Î-interactions
- Î_-interactions
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)