Spectral ergodicity and normal modes in ensembles of sparse matrices

Details Spectral ergodicity and normal modes in ensembles of sparse matrices Spectral ergodicity and normal modes in ensembles of sparse matrices

2000-09-21

arxiv.org/abs/cond-mat/0009332v1

Nucl.Phys. A687 (2001) 405-434

Physics

Condensed Matter

22 pages, 15 figures

Scientific paper

10.1016/S0375-9474(00)00576-5

We investigate the properties of sparse matrix ensembles with particular regard for the spectral ergodicity hypothesis, which claims the identity of ensemble and spectral averages of spectral correlators. An apparent violation of the spectral ergodicity is observed. This effect is studied with the aid of the normal modes of the random matrix spectrum, which describe fluctuations of the eigenvalues around their average positions. This analysis reveals that spectral ergodicity is not broken, but that different energy scales of the spectra are examined by the two averaging techniques. Normal modes are shown to provide a useful complement to traditional spectral analysis with possible applications to a wide range of physical systems.

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