Dixmier trace and the IDOS of perturbed magnetic operators

The main goal of this work is to provide a description of the trace per unit volume in terms of the Dixmier trace (regularized by the resolvent of the harmonic oscillator) for a large class of two-dimensional magnetic operators perturbed by (homogeneous) potentials. One of the payoffs of this result is the possibility of reinterpreting the density of states (DOS) of these perturbed magnetic systems via the Dixmier trace, and taking advantage of the fact that this quantity can be conveniently calculated on the basis of the Laguerrre functions that diagonalize the harmonic oscillator.