Author(s):

Erdős, László; Solovej, Jan P

Article Title: 
Uniform LiebThirring inequality for the threedimensional Pauli operator with a strong nonhomogeneous magnetic field

Affiliation 

Abstract: 
The Pauli operator describes the energy of a nonrelativistic quantum particle with spin 1/2 in a magnetic field and an external potential. A new LiebThirring type inequality on the sum of the negative eigenvalues is presented. The main feature compared to earlier results is that in the large field regime the present estimate grows with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain an optimal upper bound on the pointwise density of zero energy eigenfunctions of the Dirac operator. The main technical tools are: (i) a new localization scheme for the square of the resolvent of a general class of second order elliptic operators; (ii) a geometric construction of a Dirac operator with a constant magnetic field that approximates the original Dirac operator in a tubular neighborhood of a fixed field line. The errors may depend on the regularity of the magnetic field but they are uniform in the field strength.

Journal Title:

Annales Henri Poincare

Volume: 
5

Issue 
4

ISSN:

14240661

Publisher:

Birkhäuser

Date Published:

20040801

Start Page: 
671

End Page:

741

DOI: 
10.1007/s000230040180x

Open access: 
no 