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 
$\epsilon \ln\epsilon$.