 03452 Claudio Fernandez, Georgi Raikov
 On the Singularities of the Magnetic Spectral Shift Function at
the Landau Levels
(273K, Postscript)
Oct 3, 03

Abstract ,
Paper (src),
View paper
(auto. generated ps),
Index
of related papers

Abstract. We consider the threedimensional 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 welldefined
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.
 Files:
03452.src(
03452.keywords ,
ferrai7.ps )