M. Melgaard, E.-M. Ouhabaz, G. Rozenblum.
SPECTRAL PROPERTIES OF PERTURBED MULTIVORTEX AHARONOV-BOHM HAMILTONIANS
(433K, pdf)

ABSTRACT.  The diamagnetic inequality is established for the 
Schr\"{o}dinger operator $H_{0}^{(d)}$ in 
$L^{2}(\Rl^{d})$, $d=2,3$, describing a particle 
moving in a magnetic field generated by finitely or 
infinitely many Aharonov-Bohm solenoids located at the 
points of a discrete set in $\Rl^{2}$, e.g., a 
lattice. This fact is used to prove the Lieb-Thirring 
inequality as well as CLR-type eigenvalue estimates for 
the perturbed Schr\"{o}dinger operator 
$H_{0}^{(d)}-V$, using new Hardy type inequalities. 
Large coupling constant eigenvalue asymptotic 
formulas for the perturbed operators are also proved.