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.

Author

Grigori Rozenblioum

University of Gothenburg

Chalmers, Department of Mathematics

Michael Melgaard

Chalmers, Department of Mathematics

University of Gothenburg

Grigori Rozenblioum

Chalmers

Annales Henri Poincare

1424-0637 (ISSN) 1424-0661 (eISSN)

Vol. 5 5 979--1012-1012

Subject Categories

Mathematical Analysis

DOI

10.1007/s00023-004-0187-3

More information

Latest update

4/6/2022 5