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

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.