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Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons

T. Asaga·L. Benet·T. Rupp·H. A. Weidenmueller
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Abstract

We investigate the shape of the spectrum and the spectral fluctuations of the $k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the number of Bosons $m \to \infty$ while both $k$, the rank of the interaction, and $l$, the number of single-particle states, are kept fixed. We show that the relative fluctuations of the low spectral moments do not vanish in this limit, proving that the ensemble is non-ergodic. Numerical simulations yield spectra which display a strong tendency towards picket-fence type. The wave functions also deviate from canonical random-matrix behaviour

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T. Asaga, L. Benet, T. Rupp, H. A. Weidenmueller. 2001-07-17. Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons. https://doi.org/10.1209/epl%2Fi2001-00525-0

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