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Asymptotic Distribution of Eigenvalues for a Self-Affine String

Ingve Simonsen·Alex Hansen
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Abstract

We consider a string with fixed endpoints where the mass density and/or the elastic coefficient vary in a self-affine way as function of position. It is demonstrated how the eigenvalues in the asymptotic limit are distributed. Scaling laws for the Weyl term of the asymptotic integrated density of states is established and confirmed numerically.

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Ingve Simonsen, Alex Hansen. 1999-09-07. Asymptotic Distribution of Eigenvalues for a Self-Affine String. https://arxiv.org/abs/cond-mat/9909094

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