The spectral density of the scattering matrix of the magnetic Schrodinger operator for high energies

Hamiltonians in Magnetic Fields

20 September 15:30 - 16:30

Alexander Pushnitski - King's College London

Let $S(k)$ be the scattering matrix of the Schrodinger operator with smooth short-range electric and magnetic potentials; $k>0$ is the energy parameter. The eigenvalues of $S(k)$ are located on the unit circle. I will discuss two recent results (joint with my PhD student Daniel Bulger) on the asymptotic density of these eigenvalues as $k$ goes to infinity. It turns out that this asymptotic density can be described by explicit formulas, involving the electric potential and the magnetic vector-potentials.
Rafael D. Benguria
Pontificia Universidad Católica de Chile
Arne Jensen
Aalborg University
Georgi Raikov
Pontificia Universidad Católica de Chile
Grigori Rozenblioum
Chalmers/University of Gothenburg
Jan Philip Solovej
University of Copenhagen