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-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 ⟨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.