**
Below is the ascii version of the abstract for 03-527.
The html version should be ready soon.**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.