Delocalization and Heisenberg's uncertainty relation

G.-L. Ingold, A. Wobst, Ch. Aulbach und P. Hänggi

Eur. Phys. J. B 30, 175–179 (2002) DOI: 10.1140/epjb/e2002-00372-9

In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Harper model with its quasiperiodic potential shows a transition from extended to localized states. The difference between the two models becomes particularly apparent in phase space where Heisenberg's uncertainty relation imposes a finite resolution. Our analysis points to the relevance of the coupling between momentum eigenstates at weak potential strength for the delocalization of a quantum particle.