Symmetry Properties of the k-Body Embedded Unitary Gaussian Ensemble of Random 
Matrices

Pluhar, Z.; Weidenmüller, H.A.

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Symmetry Properties of the k-Body Embedded Unitary Gaussian Ensemble of Random Matrices

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Weidenmüller, H.A.
Prof. Hans A. Weidenmüller, Emeriti, MPI for Nuclear Physics, Max Planck Society;

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Citation

Pluhar, Z., & Weidenmüller, H. (2002). Symmetry Properties of the k-Body Embedded Unitary Gaussian Ensemble of Random Matrices. Annals of Physics, 297(2), 344-362.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0011-84DF-C

Abstract

We extend the recent study of the k-body embedded Gaussian ensembles by L. Benet, T. Rupp, and H. A. Weidenmüller (2001, Benet, Phys. Rev. Lett.87, 101601-1 and 2001, Ann. Phys. (N.Y.)292, 67) and by T. Asaga, L. Benet, T. Rupp, and H. A. Weidenmüller (cond-mat/0107363 and cond-mat/0107364). We show that central results of these papers can be derived directly from the symmetry properties of both the many-particle states and the random k-body interaction. We offer new insight into the structure of the matrix of second moments of the embedded ensemble and of the supersymmetry approach. We extend the concept of the embedded ensemble and define it purely group-theoretically.