Asymptotics of eigenvalues of the operator describing Aharonov-Bohm effect combined with homogeneous magneticfield coupled with a strong $\delta$-interaction on a loop
Honnouvo, G. ; Hounkonnou, M. N.
arXiv, 0310055 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-10-25
Classification:  Mathematical Physics 
@article{0310055,
     author = {Honnouvo, G. and Hounkonnou, M. N.},
     title = {Asymptotics of eigenvalues of the operator describing Aharonov-Bohm
  effect combined with homogeneous magneticfield coupled with a strong
  $\delta$-interaction on a loop},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0310055}
}

Honnouvo, G.; Hounkonnou, M. N. Asymptotics of eigenvalues of the operator describing Aharonov-Bohm
  effect combined with homogeneous magneticfield coupled with a strong
  $\delta$-interaction on a loop. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0310055/