Spectral properties of a generalized chGUE

Details Spectral properties of a generalized chGUE Spectral properties of a generalized chGUE

2001-03-01

arxiv.org/abs/cond-mat/0103043v1

Phys. Rev. E 64, 066121 (2001)

Physics

Condensed Matter

Disordered Systems and Neural Networks

12 pages, 3 figures

Scientific paper

10.1103/PhysRevE.64.066121

We consider a generalized chiral Gaussian Unitary Ensemble (chGUE) based on a weak confining potential. We study the spectral correlations close to the origin in the thermodynamic limit. We show that for eigenvalues separated up to the mean level spacing the spectral correlations coincide with those of chGUE. Beyond this point, the spectrum is described by an oscillating number variance centered around a constant value. We argue that the origin of such a rigid spectrum is due to the breakdown of the translational invariance of the spectral kernel in the bulk of the spectrum. Finally, we compare our results with the ones obtained from a critical chGUE recently reported in the literature. We conclude that our generalized chGUE does not belong to the same class of universality as the above mentioned model.

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