Negative discrete spectrum of perturbed multivortex Aharonov-Bohm Hamiltonians

Melgaard, M, Ouhabaz, E-M and Rozenblum, G (2004) Negative discrete spectrum of perturbed multivortex Aharonov-Bohm Hamiltonians. Annales Henri Poincare, 5 (5). pp. 979-1012. ISSN 1424-0637

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0299 Analysis. Including analytical methods connected with physical problems
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Depositing User: Michael Melgaard
Date Deposited: 19 Sep 2013 11:49
Last Modified: 19 Sep 2013 11:49
URI: http://sro.sussex.ac.uk/id/eprint/46386
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