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Correlation between eigenvalues and sorted diagonal elements of a large dimensional matrix
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DOI：10.1103/PhysRevC.79.017301.png)
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Abstract
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We show the functional dependence of eigenvalues in terms of sorted diagonal elements of a Hamiltonian matrix in the nuclear shell model (NSM), a matrix with uniform distribution and that with normal distribution. For a realistic two-body interaction, its relation is approximately expressed by a linear function, especially for the most elements in the intermediate region. We also derive their functional dependences for the uniform distribution and the normal distribution analytically. As a special case, the functional relation for the normal distribution turns out to be approximated by a hyperbolic-tangent function.
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