Random Matrices and Chaos in Nuclear Spectra

We speak of chaos in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random–matrix theory. Chaos is a typical feature of atomic nuclei and other self–bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean–field theory) plus a residual interaction. We approach the question by using a statistical approach (the two–body random ensemble): The matrix elements of the residual interaction are taken to be random variables. We show that chaos is a generic feature of the ensemble and display some of its properties, emphasizing those which differ from standard random–matrix theory. In particular, we display the existence of correlations among spectra carrying different quantum numbers. These are subject to experimental verification.