Effective Confining Potential of Quantum States in Disordered Media
Name
PhysRevLett.116.056602.pdf
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1.14 MB
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Adobe PDF
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Author(s)
Arnold, Douglas N.
David, Guy
Jerison, David
Mayboroda, Svitlana
Filoche, Marcel
Date Issued
February 2016
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Arnold, Douglas N., Guy David, David Jerison, Svitlana Mayboroda, and Marcel Filoche. “Effective Confining Potential of Quantum States in Disordered Media.” Physical Review Letters 116, no. 5 (February 5, 2016). © 2016 American Physical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.116.056602
