Delocalization and Heisenberg's uncertainty relation

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.

7 pages, 2 figures, EPL class included

References in corpus (2)

• On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems
• From ballistic motion to localization: a phase space analysis

Cited by in corpus (20)

• Exponential localization in one-dimensional quasiperiodic optical lattices
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasi-periodic potentials
• On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems
• Dynamical evolution in a one-dimensional incommensurate lattice with $\mathcal{P}\mathcal{T}$ symmetry
• Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Wave interactions in localizing media - a coin with many faces
• Critical exponents of the disorder-driven superfluid-insulator transition in one-dimensional Bose-Einstein condensates
• Maximally localized Wannier functions for ultracold atoms in one-dimensional double-well periodic potentials
• Phase space signatures of the Anderson transition
• Finite-size effects in Anderson localization of one-dimensional Bose-Einstein condensates
• Signatures of the single particle mobility edge in the ground state properties of Tonks-Girardeau and non-interacting Fermi gases in a bichromatic potential
• Continuous-time quantum walks in the presence of a quadratic perturbation
• Localization from quantum interference in one-dimensional disordered potentials
• Almost mobility edges and existence of critical regions in one-dimensional quasiperiodic lattices
• Phase transition in a Aubry-Andre system with rapidly oscillating magnetic field
• Lattice bosons in a quasi-disordered environment: The effects of next-nearest-neighbor hopping on localization and Bose-Einstein condensation
• Lattice bosons in a quasi-disordered environment