The Integrated Density of States for an Interacting Multiparticle Homogeneous Model and Applications to the Anderson Model

Abstract EN

For a system of n interacting particles moving in the background of a “homogeneous” potential, we show that if the single particle Hamiltonian admits a density of states, so does the interacting n-particle Hamiltonian.

Moreover, this integrated density of states coincides with that of the free particle Hamiltonian.

For the interacting n-particle Anderson model, we prove regularity properties of the integrated density of states by establishing a Wegner estimate.