Abstract
We study the spin‐dependent widths of random Hamiltonians and derive closed expressions for their distributions and the correlations between them. This is facilitated by the introduction of linear combinations of two‐body operators that are orthogonal under the canonical scalar product for matrices. Considering six fermions in a single j‐shell, we find that the width of spin‐0 Hamiltonians exhibits a relatively large average value, relatively small fluctuations, and is strongly correlated to other low‐spin widths. The width of maximum spin in contrast has the largest average value and largest fluctuations. An approximate proportionality between spectral width and ground state energies explains the spin‐0 dominance in the shell model with random interactions.
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