Claudio Fernandez, Georgi Raikov
On the Singularities of the Magnetic Spectral Shift Function at 
the Landau Levels
(273K, Postscript)

ABSTRACT.  We consider the three-dimensional Schr\"odinger operators $H_0$ and 
 $H_{\pm}$ where $H_0 = (i\nabla + A)^2 - b$, $A$ is a magnetic potential 
 generating a constant magnetic field of strength $b>0$, and $H_{\pm} = H_0 \pm 
 V$ where $V \geq 0$ decays fast enough at infinity. 
Then, A. Pushnitski's representation of the spectral shift 
 function (SSF) for 
the pair of operators $H_{\pm}$, $H_0$ is well-defined 
for energies $E \neq 2qb$, $q \in {\mathbb Z}_+$. We study the 
 behaviour of the associated representative of the equivalence 
 class determined by the SSF, in a neighbourhood of the Landau 
 levels $2qb$, $q \in {\mathbb Z}_+$. Reducing our analysis to the study of the 
 eigenvalue asymptotics for a family of compact operators of Toeplitz 
 type, we establish a relation between the type of 
 the singularities of the SSF at the Landau levels and the decay rate 
 of $V$ at infinity.