02-13 Pavel Exner and Kazushi Yoshitomi
Persistent currents for 2D Schr\"odinger operator with a strong $\delta$-interaction on a loop (36K, LaTeX 2e) Jan 9, 02
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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.

Files: 02-13.tex