Pavel Exner and Kazushi Yoshitomi
Persistent currents for 2D Schr\"odinger operator
with a strong $\delta$-interaction on a loop
(36K, LaTeX 2e)
ABSTRACT. We investigate the two-dimensional magnetic
Schr\"odinger operator $H_{B,\beta}=\left(-i\nabla-A\right)^2
-\beta\delta(\cdot-\Gamma)$, where $\Gamma$ is a smooth loop and
the vector potential $A$ corresponds to a homogeneous magnetic
field $B$ perpendicular to the plane. The asymptotics of negative
eigenvalues of $H_{B,\beta}$ for $\beta\to\infty$ is found. It
shows, in particular, that for large enough positive $\beta$ the
system exhibits persistent currents.