Browsing by Subject "delta-interactions"

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Access status: Open Access ,
Singular continuous spectrum of half-line Schrödinger operators with point interactions on a sparse set
(2011) Lotoreichik, Vladimir
We say that a discrete set $X = \{ x_n \}_{n\in \mathbb{N}_0}$ on the half-line $0 = x_0 \lt x_1 \lt x_2 \lt x_3 \lt ... \lt x_n \lt ... \lt +\infty$ is sparse if the distances $\Delta x_n = x_{n+1}- x_n$ between neighbouring points satisfy the condition $\frac{\Delta x_n}{\Delta x_{n-1}} \to +\infty$. In this paper half-line Schrödinger operators with point $\delta#- and $\delta'$- interactions on a sparse set are considered. Assuming that strengths of point interactions tend to $\infty$ we give simple sufficient conditions for such Schrödinger operators to have non-empty singular continuous spectrum and to have purely singular continuous spectrum, which coincides with $\mathbb{R}_+$.