Abstract
We prove that, for large disorder or near the band tails, the spectrum of the Anderson tight binding Hamiltonian with diagonal disorder consists exclusively of discrete eigenvalues. The corresponding eigenfunctions are exponentially well localized. These results hold in arbitrary dimension and with probability one. In one dimension, we recover the result that all states are localized for arbitrary energies and arbitrarily small disorder. Our techniques extend to other physical systems which exhibit localization phenomena, such as infinite systems of coupled harmonic oscillators, or random Schrödinger operators in the continuum.
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Communicated by A. Jaffe
Work supported in part by National Science Foundations grant MCS-8108814 (A03).
Work supported in part by National Science Foundation grant DMR 81-00417.
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Fröhlich, J., Martinelli, F., Scoppola, E. et al. Constructive proof of localization in the Anderson tight binding model. Commun.Math. Phys. 101, 21–46 (1985). https://doi.org/10.1007/BF01212355
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DOI: https://doi.org/10.1007/BF01212355