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- W2949133645 abstract "We prove lower bounds on the localization length of eigenfunctions in the three-dimensional Anderson model at weak disorders. Our results are similar to those obtained by Schlag, Shubin and Wolff for dimensions one and two. We prove that with probability one, most eigenfunctions have localization lengths bounded from below by $O(frac{lambda^{-2}}{logfrac1lambda})$, where $lambda$ is the disorder strength. This is achieved by time-dependent methods which generalize those developed by Erdos and Yau to the lattice and non-Gaussian case. In addition, we show that the macroscopic limit of the corresponding lattice random Schrodinger dynamics is governed by the linear Boltzmann equations." @default.
- W2949133645 created "2019-06-27" @default.
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- W2949133645 date "2003-05-26" @default.
- W2949133645 modified "2023-09-27" @default.
- W2949133645 title "Localization Lengths and Boltzmann Limit for the Anderson Model at Small Disorders in Dimension 3" @default.
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