Absolute continuity of the integrated density of states of the quantum Lorentz gas for a class of repulsive potentials

For a class of repulsive potentials, for instance of the type j(x)= Ixl^-k[1+x²]^-l(k,l positive, in a certain range) in the random Schrödinger operators H(w)=p²+V(x,w)=p²+Š_jj(x-x_j), acting in L²(R^d), with Poisson distributed x_jS (the quantum Lorentz gas), we show that the integrated density or states N(E) is absolutely continuous for E>zr<j>. Here is <j> the integral of j over R^d, r the averaged density of points x_j and z>0 depends on j and d. In the above example, z=(d/k)². Our method makes use of a Fock space representation for the Poisson random system, recently developed by Maassen and the author. Within this Fock space formalism the Mourre commutator method is then employed to obtain the announced result.