Hamburg 2001 – scientific programme
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.2: Poster
Thursday, March 29, 2001, 15:45–18:15, Foyer S\ 3
Spectral ergodicity and normal modes in ensembles of sparse matrices — •Markus Saltzer1, Andrew D. Jackson2, Carlos Mejia-Monasterio3, Thomas Rupp4, and Thomas Wilke2 — 1Fakultät für Physik, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany — 2The Niels Bohr Institute, Belgdamsvej 17, DK-2100 Copenhagen, Danmark — 3Centro de Ciencias Fisicas, UNAM, Apartado Postal 48-3, Cuernavaca, Mexico — 4Max-Planck-Institut für Kerphysik, Postfach 103980, D-69029 Heidelberg, Germany
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.