Eigenfunction Statistics of Complex Systems: A Common Mathematical Formulation

Pragya Shukla

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Eigenfunction Statistics of Complex Systems: A Common Mathematical Formulation

Pragya Shukla

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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.

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Pragya Shukla. 2007-05-04. Eigenfunction Statistics of Complex Systems: A Common Mathematical Formulation. https://arxiv.org/abs/cond-mat/0505007

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