Localization Lengths and Boltzmann Limit for the Anderson Model at Small Disorders in Dimension 3

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dc.creatorChen, Thomas
dc.date2003-05-26
dc.date2005-03-24
dc.date.accessioned2026-07-07T06:19:38Z
dc.date.available2026-07-07T06:19:38Z
dc.descriptionWe 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 $O(\frac{λ^{-2}}{\log\frac1λ})$, where $λ$ is the disorder strength. This is achieved by time-dependent methods which generalize those developed by Erdös and Yau to the lattice and non-Gaussian case. In addition, we show that the macroscopic limit of the corresponding lattice random Schrödinger dynamics is governed by the linear Boltzmann equations.
dc.descriptionAMS LaTeX, 45 pages, 3 figures. Final version, crossing estimates corrected. To appear in J. Stat. Phys
dc.identifierhttps://arxiv.org/abs/math-ph/0305051
dc.identifierhttp://arxiv.org/abs/math-ph/0305051
dc.identifierJ. Stat. Phys. 120 (1-2), 279 - 337 (2005).
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/95094
dc.subjectMathematical Physics
dc.subjectSpectral Theory
dc.subject81Q10, 76Y05
dc.titleLocalization Lengths and Boltzmann Limit for the Anderson Model at Small Disorders in Dimension 3
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