Phase-space signatures of the Anderson transition

We use the inverse participation ratio based on the Husimi function to perform a phase-space analysis of the Anderson model in one, two, and three dimensions. Important features of the quantum states remain observable in phase space in the large system size limit, while they would be lost in a real- or momentum-space description. From perturbative approaches in the limits of weak and strong disorder, we find that the appearance of a delocalization-localization transition is connected to the coupling, by a weak potential, of momentum eigenstates which are far apart in momentum space. While this is fully consistent with the known dependence of the existence of the Anderson transition on dimensionality, the resulting criterion can be applied to other models as well. The phase-space approach thus sheds new light on the metal-insulator transition.