Anderson–Bernoulli Localization at Large Disorder on the 2D Lattice

We consider the Anderson model at large disorder on Z 2 where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These finitely many energies are Dirichlet eigenvalues of the minus Laplacian restri...

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Veröffentlicht in:	Communications in mathematical physics 2022-07, Vol.393 (1), p.151-214
1. Verfasser:	Li, Linjun
Format:	Artikel
Sprache:	eng
Schlagworte:	Anderson localization Classical and Quantum Gravitation Complex Systems Dirichlet problem Eigenvalues Mathematical and Computational Physics Mathematical Physics Physics Physics and Astronomy Quantum Physics Relativity Theory Theoretical
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Zusammenfassung:	We consider the Anderson model at large disorder on Z 2 where the potential has a symmetric Bernoulli distribution. We prove that Anderson localization happens outside a small neighborhood of finitely many energies. These finitely many energies are Dirichlet eigenvalues of the minus Laplacian restricted on some finite subsets of Z 2 .
ISSN:	0010-3616 1432-0916
DOI:	10.1007/s00220-022-04366-1