Abstract.
The diamagnetic inequality is established for the Schrödinger operator H(d)0 in L2 \((\mathbb{R}^d ),\) 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 \(\mathbb{R}^2 ,\) 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(d)0−V, using new Hardy type inequalities. Large coupling constant eigenvalue asymptotic formulas for the perturbed operators are also proved.
Article PDF
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Bernard Helffer
submitted 02/12/03, accepted 12/03/04
Rights and permissions
About this article
Cite this article
Melgaard, M., Ouhabaz, EM. & Rozenblum, G. Negative Discrete Spectrum of Perturbed Multivortex Aharonov-Bohm Hamiltonians. Ann. Henri Poincaré 5, 979–1012 (2004). https://doi.org/10.1007/s00023-004-0187-3
Issue Date:
DOI: https://doi.org/10.1007/s00023-004-0187-3