Asymptotics of eigenvalues of the operator describing Aharonov-Bohm effect combined with homogeneous magneticfield coupled with a strong $δ$-interaction on a loop

Details Asymptotics of eigenvalues of the operator describing Aharonov-Bohm effect combined with homogeneous magneticfield coupled with a strong $δ$-interaction on a loop Asymptotics of eigenvalues of the operator describing Aharonov-Bohm effect combined with homogeneous magneticfield coupled with a strong $δ$-interaction on a loop

2003-10-25

arxiv.org/abs/math-ph/0310055v1

Physics

Mathematical Physics

11 pages

Scientific paper

We investigate the two-dimensional magnetic operator $H_{c_0,B,\beta} = {(-i\nabla -A)}^{2}-\beta\delta(.-\Gamma),$ where $\Gamma$ is a smooth loop. The vector potential has the form $A=c_0\bigg(\frac{-y}{{x^2+y^2}}; \frac{x}{{x^2+y^2}} \bigg)+ \frac{B}{2}\bigg(-y; x\bigg) $; $B>0,$ $c_0\in]0;1[$. The asymptotics of negative eigenvalues of $H_{c_0,B,\beta}$ 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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