Negative discrete spectrum of perturbed multivortex Aharonov-Bohm Hamiltonians

The diamagnetic inequality is established for the Schrödinger operator H (d) 0 in L 2 (Rd), 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 R2, e.g., a lattice. This fact is used to prove the Lieb-Thirring inequality as well as CLR-type eigenvalue estimates for the perturbed Schrödinger operator H (d) 0-V, using new Hardy type inequalities. Large coupling constant eigenvalue asymptotic formulas for the perturbed operators are also proved.