03-527 M. Melgaard, E.-M. Ouhabaz, G. Rozenblum.

SPECTRAL PROPERTIES OF PERTURBED MULTIVORTEX AHARONOV-BOHM HAMILTONIANS (433K, pdf) Dec 5, 03

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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.

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