 0213 Pavel Exner and Kazushi Yoshitomi
 Persistent currents for 2D Schr\"odinger operator
with a strong $\delta$interaction on a loop
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Jan 9, 02

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Abstract. We investigate the twodimensional magnetic
Schr\"odinger operator $H_{B,\beta}=\left(i\nablaA\right)^2
\beta\delta(\cdot\Gamma)$, 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.
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