Shell Model with Random Interactions

Abstract

The standard description of a many-body quantum system is based on the mean field and residual interactions. As excitation energy grows, the high level density makes any residual interaction effectively strong, independent particle configurations mix, and the energy spectrum acquires local features predicted by random matrix theory (RMT) [1, 2, 3], whereas neighboring stationary states “look the same” [4]. This picture of universal quantum chaos is applicable to nuclei, atoms, solid state microdevices, quantum computing schemes and quantum field models. At low excitation energy the stationary states are less mixed, and coherent effects are strongly pronounced. According to conventional wisdom, the quantum numbers and ordering of the low-lying states are not universal being determined by the specifics of the system, its symmetry and the coherent part of the residual interaction. Thus, all even-even nuclei has the ground state (g.s.) spin J ₀ = 0; practically always the g.s. isospin T ₀ takes the lowest possible value. This is assumed to be a consequence of the strong attractive pairing correlations.