Negative discrete spectrum of perturbed multivortex Aharonov-Bohm Hamiltonians.

Journal article, 2004

The diamagnetic inequality is established for the Schrödinger operator H 0 (d) in L 2 (ℝ 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 ℝ 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 Schrödinger operator H 0(d) - V, using new Hardy type inequalities. Large coupling constant eigenvalue asymptotic formulas for the perturbed operators are also proved.