On the distribution of linear combinations of eigenvalues of the Anderson model

2008/08/31 by Shmuel Fishman, Fishman, Shmuel, Yevgeny Krivolapov +3
Mathematics · Physics and Astronomy · #81V99 #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #msc:81V99

paper · pdf · doi:10.48550/arxiv.0809.0121

12 pages, 0 figures

arxiv created 2008/08/31 · arxiv updated 2009/12/01

Abstract

Probabilistic estimates on linear combinations of eigenvalues of the one dimensional Anderson model are derived. So far only estimates on the density of eigenvalues and of pairs were found by Wegner and by Minami. Our work was motivated by perturbative explorations of the Nonlinear Schroedinger Equation, where linear combinations of eigenvalues are the denominators and evaluation of their smallness is crucial.

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