Negative Discrete Spectrum of Perturbed Multivortex Aharonov-Bohm Hamiltonians |
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| Authors: | M Melgaard E-M Ouhabaz G Rozenblum |
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| Institution: | (1) Department of Mathematics, Uppsala University, Polacksbacken, S-751 06 Uppsala, Sweden;(2) Laboratoire Bordelais d Analyse et Géométrie, Université de Bordeaux 1, 351, Cours de la Libération, F-33405 Talence cedex, France;(3) Department of Mathematics, Chalmers University of Technology and University of Gothenburg, Eklandagatan 86, S-412 96 Gothenburg, Sweden |
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| Abstract: | The diamagnetic inequality is established for the Schrödinger operator H(d)0 in L2
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
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.Communicated by Bernard Helffersubmitted 02/12/03, accepted 12/03/04 |
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