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

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

2002-01-09

arxiv.org/abs/math-ph/0201020v1

J. Phys. A35 (2002), 3479-3487

Physics

Mathematical Physics

LaTeX 2e, 13 pages

Scientific paper

10.1088/0305-4470/35/15/309

We investigate the two-dimensional magnetic Schr\"odinger 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.

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