Effective Confining Potential of Quantum States in Disordered Media

Douglas N. Arnold, Guy David, David Jerison, Svitlana Mayboroda, and Marcel Filoche
Phys. Rev. Lett. 116, 056602 – Published 5 February 2016
PDFHTMLExport Citation

Abstract

The amplitude of localized quantum states in random or disordered media may exhibit long-range exponential decay. We present here a theory that unveils the existence of an effective potential which finely governs the confinement of these states. In this picture, the boundaries of the localization subregions for low energy eigenfunctions correspond to the barriers of this effective potential, and the long-range exponential decay characteristic of Anderson localization is explained as the consequence of multiple tunneling in the dense network of barriers created by this effective potential. Finally, we show that Weyl’s formula based on this potential turns out to be a remarkable approximation of the density of states for a large variety of one-dimensional systems, periodic or random.

  • Figure
  • Figure
  • Figure
  • Received 12 May 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.056602

© 2016 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Douglas N. Arnold1,*, Guy David2,†, David Jerison3,‡, Svitlana Mayboroda1,§, and Marcel Filoche4,∥

  • 1School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, USA
  • 2Université Paris–Sud, Laboratoire de Mathématiques, CNRS, UMR 8658, Orsay F-91405, France
  • 3Mathematics Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 4Physique de la Matière Condensée, Ecole Polytechnique, CNRS, Palaiseau F-91128, France

  • *arnold@umn.edu
  • guy.david@math.u-psud.fr
  • jerison@math.mit.edu
  • §svitlana@math.umn.edu
  • marcel.filoche@polytechnique.edu

Comments & Replies

Comment on “Effective Confining Potential of Quantum States in Disordered Media”

Alain Comtet and Christophe Texier
Phys. Rev. Lett. 124, 219701 (2020)

Filoche et al. Reply:

M. Filoche, D. Arnold, G. David, D. Jerison, and S. Mayboroda
Phys. Rev. Lett. 124, 219702 (2020)

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 116, Iss. 5 — 5 February 2016

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review Letters

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×