Spectral asymptotics of a weakly perturbed Landau Hamiltonian

Alexander Pushnitski Loughborough University, U.K.

If the Landau Hamiltonian (i.e. the two dimentional Schrodinger operator with constant magnetic field) is perturbed by adding a compactly supported potential, the spectrum of the resulting operator consists of clusters of eigenvalues accumulating to the Landau levels. The rate of accumulation of eigenvalues in a particular spectral cluster was studied recently in two papers [G.Raikov-S.Warzel] and [M.Melgaard-G.Rozenblum]. We give a more detailed description of the rate of accumulation of eigenvalues, relating it to the logarithmic capacity of the support of the perturbation potential. This is a joint work with N.Filonov.