Author(s):

Erdős, László; Solovej, Jan P

Article Title: 
Magnetic LiebThirring inequalities with optimal dependence on the field strength

Affiliation 

Abstract: 
The Pauli operator describes the energy of a nonrelativistic quantum particle with spin in a magnetic field and an external potential. Bounds on the sum of the negative eigenvalues are called magnetic LiebThirring (MLT) inequalities. The purpose of this paper is twofold. First, we prove a new MLT inequality in a simple way. Second, we give a short summary of our recent proof of a more refined MLT inequality(8) and we explain the differences between the two results and methods. The main feature of both estimates, compared to earlier results, is that in the large field regime they grow with the optimal (first) power of the strength of the magnetic field. As a byproduct of the method, we also obtain optimal upper bounds on the pointwise density of zero energy eigenfunctions of the Dirac operator.

Keywords: 
kernel of Dirac operator; nonhomogeneous magnetic field

Journal Title:

Journal of Statistical Physics

Volume: 
116

Issue 
14

ISSN:

15729613

Publisher:

Springer

Date Published:

20040801

Start Page: 
475

End Page:

506

DOI: 
10.1023/B:JOSS.0000037216.45270.1d

Open access: 
no 