Eigenfunction Statistics of Complex Systems: A Common Mathematical Formulation
Abstract
We derive a common mathematical formulation for the eigenfunction statistics of Hermitian operators, represented by a multi-parametric probability density. The system-information in the formulation enters through two parameters only, namely, system size and the complexity parameter, a function of all system parameter including size. The behavior is contrary to the eigenvalue statistics which is sensitive to complexity parameter only and shows a single parametric scaling. The existence of a mathematical formulation, of both eigenfunctions and eigenvalues, common to a wide range of complex systems indicates the possibility of a similar formulation for many physical properties. This also suggests the possibility to classify them in various universality classes defined by complexity parameter.
Cite
@article{arxiv.cond-mat/0505007,
title = {Eigenfunction Statistics of Complex Systems: A Common Mathematical Formulation},
author = {Pragya Shukla},
journal= {arXiv preprint arXiv:cond-mat/0505007},
year = {2007}
}
Comments
16 Figures, Several Changes, Many new sections and figures included, conclusion slightly changed