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.Comment: 17 pages, 20 figures, colloquium article, submitted to Reviews of
Modern Physic
