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

Pavel Exner·Kazushi Yoshitomi
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Abstract

We investigate the two-dimensional magnetic Schrödinger operator $H_{B,β}=(-i\nabla-A)^2 -βδ(\cdot-Γ)$, where $Γ$ 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 $H_{B,β}$ for $β\to\infty$ is found. It shows, in particular, that for large enough positive $β$ the system exhibits persistent currents.

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Pavel Exner, Kazushi Yoshitomi. 2002-01-09. Persistent currents for 2D Schrödinger operator with a strong $δ$-interaction on a loop. https://doi.org/10.1088/0305-4470%2F35%2F15%2F309

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