Persistent currents for 2D Schrödinger operator with a strong $\delta$-interaction on a loop

Abstract

We investigate the two-dimensional magnetic Schrödinger operator $H_{B,\beta }=(-i\nabla -A{)}^2-\beta \delta (\cdot -\Gamma )$, 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.

LaTeX 2e, 13 pages

References in corpus (1)

• Asymptotics of eigenvalues of the Schroedinger operator with a strong delta-interaction on a loop

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