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

Abstract

For a class of repulsive potentials, for instance of the type phi (x)= mod x mod - kappa (1+x2)- lambda ( kappa , lambda positive, in a certain range) in the random Schrodinger operators H( omega )=p2+V (x, omega )=P2+ Sigma j phi (x-xj), acting in L2 (Rd), with Poisson distributed xjs (the quantum Lorentz gas), we show that the integrated density of states N(E) is absolutely continuous for E> zeta rho ( phi ). Here is ( phi ) the integral of phi over Rd, rho the averaged density of points xj and zeta >0 depends on phi and d. In the above example, zeta =(d/ kappa )2. Our method makes use of a Fock space representation for the Poisson random system, recently developed by Maassen and the author (1993). Within this Fock space formalism the Mourre commutator method is then employed to obtain the announced result.