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+Šjj(x-xj), acting in L2(Rd), with Poisson distributed xjS (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 Rd, r the averaged density of points xj 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.
|Journal||J. Phys. A|
Tip, A. (1994). Absolute continuity of the integrated density of states of the quantum Lorentz gas for a class of repulsive potentials. J. Phys. A, 27, 1057–1069.