RANDOM MAGNETIC-IMPURITIES AND THE DELTA-IMPURITY PROBLEM

One considers the effect of disorder on the 2-dimensional density of s tates of an electron of charge e in a constant magnetic field superpos ed onto a Poissonnian random distribution of point vortices carrying a flux phi (alpha = e phi/2 pi is the dimensionless coupling constant). If the electron Hilbert space is restricted to the Lowest Landau Leve l (LLL) of the total average magnetic field, the random magnetic impur ity problem is mapped onto a contact delta impurity problem. Particula r features of the average density of states are then interpreted in te rms of the microscopic eigenstates of the N impurity Hamiltonian. The deformation of the density of states with respect to the density of im purities manifests itself by the progressive depopulation of the LLL. A Brownian motion analysis of the model, based on Brownian probability distributions for arithmetic area winding sectors, is also proposed. In the case alpha = +/-1/2, the depletion of states at the bottom of t he spectrum is materialized by a Lifschitz tail in the average density of states.