KMS states and the chemical potential for disordered systems

We extend the theory of the chemical potential associated to a compact separable gauge group to the case of disordered quantum systems. This is done in the natural framework of operator algebras. Among the other results, we show that the chemical potential does not depend on the disorder. The situation of the $n$--torus is treated in some detail. Indeed, provided that the zero--point is fixed independently on the disorder, the chemical potential is intrinsically defined in terms of the direct integral decomposition of the Connes--Radon--Nikodym cocycle associated to the KMS state $\omega$ and its trasforms $\omega\circ\rho$ by the localized automorphisms $\rho$ of the observable algebra, carrying the abelian charges of the model under consideration. This description parallels the analogous one relative to the usual (i.e. non disordered) quantum models.