### Abstract

Properties and structure of the Hamiltonian matrix of a realistic many-body

quantum chaotic system (the rare-earth atom of Ce) are analyzed and compared

with those assumed in band random matrix theories. The sparsity of the matrix

and the behaviour of the mean squared matrix elements ⟨H

quantum chaotic system (the rare-earth atom of Ce) are analyzed and compared

with those assumed in band random matrix theories. The sparsity of the matrix

and the behaviour of the mean squared matrix elements ⟨H

_{ij}^{2}⟩_{|i-j|=Δ}as function of the distance |i-j| from the diagonal are studied. Fitting ⟨H_{ij}^{2}⟩_{|i-j|=Δ}with the exponent H_{0}^{2}exp(-Δ/b) yields the bandwidths of b=53.5 and 78 for the matrices of J^{π}=4^{+}, 4^{- }states respectively.Original language | English |
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Pages (from-to) | 5667-5670 |

Journal | Physical Review E |

Volume | 52 |

DOIs | |

Publication status | Published - 01 Nov 1995 |

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## Cite this

Gribakina, A. A., Flambaum, V. V., & Gribakin, G. F. (1995). Band structure of the Hamiltonian matrix of a real ‘‘chaotic’’ system: The Ce atom.

*Physical Review E*,*52*, 5667-5670. https://doi.org/10.1103/PhysRevE.52.5667