Delocalization and Heisenberg's uncertainty relation

2002/05/02 by Gert-Ludwig Ingold, Gert‐Ludwig Ingold, Andre Wobst +4
Physics and Astronomy · #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat.dis-nn #cond-mat.stat-mech

paper · pdf · doi:10.1140/epjb/e2002-00372-9

published as Eur. Phys. J. B 30, 175 (2002) · 7 pages, 2 figures, EPL class included

arxiv created 2002/05/02 · openalex publication_date 2002/11/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

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.

Citations

• Rényi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

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