Band structure of the Hamiltonian matrix of a real ‘‘chaotic’’ system: The Ce atom

Properties and structure of the Hamiltonian matrix of a realistic many-bodyquantum chaotic system (the rare-earth atom of Ce) are analyzed and comparedwith those assumed in band random matrix theories. The sparsity of the matrixand the behaviour of the mean squared matrix elements ⟨Hij2⟩|i-j|=Δ as function of the distance |i-j| from the diagonal are studied. Fitting ⟨Hij2⟩|i-j|=Δ with the exponent H02 exp(-Δ/b) yields the bandwidths of b=53.5 and 78 for the matrices of Jπ=4+, 4- states respectively.