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

Details Asymptotics of eigenvalues of the Aharonov-Bohm operator with a strong $δ$-interaction on a loop Asymptotics of eigenvalues of the Aharonov-Bohm operator with a strong $δ$-interaction on a loop

2003-06-26

arxiv.org/abs/math-ph/0306067v4

Physics

Mathematical Physics

9 pages

Scientific paper

10.1088/0305-4470/37/3/012

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 $\beta \longrightarrow +\infty$ is found. We also prove that for large enough positive value of $\beta$ the system exhibits persistent currents.

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