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

Delocalization and Heisenberg's uncertainty relation

Institut für Physik, Universität Augsburg, Universitätsstrasse 1, 86135 Augsburg, Germany

Corresponding author: ^a Gert.Ingold@physik.uni-augsburg.de

Received: 3 May 2002
Revised: 2 October 2002
Published online: 29 November 2002

Abstract

In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Aubry-André 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.