Pavel Exner and Sylwia Kondej
Hiatus perturbation for a singular Schr\"odinger operator with
an interaction supported by a curve in $\mathbb{R}^3$
(84K, LaTeX)
ABSTRACT. We consider Schr\"odinger operators in $L^2(\mathbb{R}^3)$ with a
singular interaction supported by a finite curve $\Gamma$. We
present a proper definition of the operators and study their
properties, in particular, we show that the discrete spectrum can
be empty if $\Gamma$ is short enough. If it is not the case, we
investigate properties of the eigenvalues in the situation when
the curve has a hiatus of length $2\epsilon$. We derive an
asymptotic expansion with the leading term which a multiple of
$\epsilon \ln\epsilon$.