Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices

Details Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices Non-Universal Behavior of the k-Body Embedded Gaussian Unitary Ensemble of Random Matrices

2000-10-26

arxiv.org/abs/cond-mat/0010425v2

Phys.Rev.Lett. 87 (2001) 010601

Physics

Condensed Matter

4 pages, no figures, revised version including a new proof of one of our main claims

Scientific paper

10.1103/PhysRevLett.87.010601

Using a novel approach, we investigate the shape of the average spectrum and the spectral fluctuations of the $k$-body embedded unitary ensemble in the limit of large matrix dimension. We identify the transition point between semicircle and Gaussian shape. The transition also affects the spectral fluctuations which deviate from Wigner-Dyson form and become Poissonian in the limit $k << m << l$. Here $m$ is the number of Fermions and $l$ the number of degenerate single-particle states.

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