Browsing by Subject "spectral gap"

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Access status: Open Access ,
Decisiveness of the spectral gaps of periodic Schrödinger operators on the dumbbell-like metric graph
(2015) Niikuni, Hiroaki
In this paper, we consider periodic Schrödinger operators on the dumbbell-like metric graph, which is a periodic graph consisting of lines and rings. Let one line and two rings be in the basic period. We see the relationship between the structure of graph and the band-gap spectrum.
Access status: Open Access ,
On the spectrum of periodic perturbations of certain unbounded Jacobi operators
(2016) Sahbani, Jaouad
It is known that a purely off-diagonal Jacobi operator with coefficients $a_n=n^{\alpha}$, $\alpha\in(0,1]$ has a purely absolutely continuous spectrum filling the whole real axis. We show that a 2-periodic perturbation of these operators creates a non trivial gap in the spectrum.