shell. In both examples the probability for a given state to become the ground state is shown to be related to a geometric property of a polygon or polyhedron which is entirely determined by particle number, shell size, and symmetry character of the states. The extensions to more general situations are discussed.

DOI: 10.1103/physrevc.66.061302

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j=\frac{7}{2}

The observed preponderance of ground states with angular momentum

L=0

in many-body quantum systems with random two-body interactions is analyzed in terms of correlation coefficients (covariances) among different eigenstates. It is shown that the geometric analysis of Chau et al. can be interpreted in terms of correlations (covariances) between energy eigenvalues, thus providing an entirely statistical explanation of the distribution of ground state angular momenta of randomly interacting quantum systems that, in principle, is valid for both fermionic and bosonic systems. The method is illustrated for the interacting boson model.

Low-lying states in nuclei are investigated using an ensemble of random interactions. Both in the nuclear shell model and in the interacting boson model we find a dominance of

J^P=0^+

ground states. It is shown that this feature is not due to time reversal symmetry. In the shell model, evidence is found for the occurrence of pairing properties, and in the interacting boson model for both vibrational and rotational band structures. Our results suggest that these features represent general and robust properties of the model space, and do not depend on details of the interactions.

In this paper we revisit spin

I

ground state probabilities (denoted by

P(I))

of a few integrable systems under random interactions. We obtain explicit and simple formulas of

P(I)

for

d

-boson systems and fermions in a

j=5/2

shell.