Localization for random potentials supported on a subspace |
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| Authors: | V Grinshpun |
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| Institution: | (1) Institut de Mathématiques de Paris-Jussieu, UMR C9994, Physique mathématique et Géométrie, Université Paris 7 Denis Diderot, case 7012, 2 Place Jussieu, 75251 Paris Cedex 05, France;(2) Present address: Mathematical Division, Institute for Low Temperature Physics, 47 Lenin Avenue, Kharkov, Ukraine |
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| Abstract: | We consider the lattice Schrödinger operator acting onl
2 (
d
) with random potential (independent, identically distributed random variables), supported on a subspace of dimension 1  v <d. We use the multiscale analyses scheme to prove that this operator exhibits exponential localization at the edges of the spectrum for any disorder or outside the interval -2d, 2d] for sufficiently high disorder. |
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| Keywords: | 47N55 82Bxx 60H25 82D35 |
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