Asymptotics of eigenvalues of the Aharonov-Bohm operator with a strong $\delta$-interaction on a loop

Abstract

We investigate the two-dimensional Aharonov-Bohm operator $H_{c_0,\beta }={(-i\nabla -A)}^2-\beta \delta (.-\Gamma ),$ where $\Gamma$ is a smooth loop and $A$ is the vector potential which corresponds to Aharonov-Bohm potential. The asymptotics of negative eigenvalues of $H_{c_0,\beta }$ for $\beta ⟶+\infty$ is found. We also prove that for large enough positive value of $\beta$ the system exhibits persistent currents.

9 pages

References in corpus (2)

• Asymptotics of eigenvalues of the Schroedinger operator with a strong delta-interaction on a loop
• Persistent currents for 2D Schrödinger operator with a strong $\delta$-interaction on a loop