Hamburg 2001 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 23: Quantenchaos

DY 23.8: Vortrag

Dienstag, 27. März 2001, 12:15–12:30, S 7

Spectral ergodicity and normal modes in chiral random matrices and lattice gauge simulations — •Thomas Wilke and Andrew D. Jackson — The Niels Bohr Institute, Belgdamsvej 17, DK-2100 Copenhagen, Danmark

Spectra of the non-abelian Dirac operator obtained from lattice gauge calculations have seen to show non-ergodic spectral properties, i.e. differences in ensemble and spectral averages of spectral correlators. This observed violation of spectral ergodicity may not be disturbing given the intrinsic nature of ensemble averaging in lattice gauge calculations.

However, recent results from random-matrix theory indicate that in certain systems the violation of spectral ergodicity is merely apparent. This can be understood from the normal modes of the corresponding spectra. It is not clear so far whether these results can be carried over to numerical simulations on the lattice.

We set up a model of chiral sparse random matrices. Some essential results from lattice gauge simulations can be reproduced. Performing a normal mode analysis it becomes clear that there is no breaking of spectral ergodicty in such models. This could lead to a deeper understanding of the statistical behaviour of lattice gauge simulations and finally to a simplification and reduce of computer time of such calculations.