From ballistic motion to localization: a phase space analysis

A. Wobst, G.-L. Ingold, P. Hänggi, and D. Weinmann

Eur. Phys. J. B 27, 11–14 (2002) DOI: 10.1140/epjb/e20020125

We introduce phase space concepts to describe quantum states in a disordered system. The merits of an inverse participation ratio defined on the basis of the Husimi function are demonstrated by a numerical study of the Anderson model in one, two, and three dimensions. Contrary to the inverse participation ratios in real and momentum space, the corresponding phase space quantity allows for a distinction between the ballistic, diffusive, and localized regimes on a unique footing and provides valuable insight into the structure of the eigenstates.