  There is a newly emerging understanding that in the chaotic domain of
isolated finite interacting many particle systems smoothed densities define the
statistical description of these systems and these densities follow from
embedded (two-body) random matrix ensembles and their various deformations.
These ensembles predict that the smoothed form of matrix elements of a
transition operator between the chaotic eigenstates weighted by the densities
at the two ends (i.e. the bivariate strength density) will be a bivariate
Gaussian with the bivariate correlation coefficient arising out of the
non-commutability of the hamiltonian and the transition operator involved. The
ensemble theory extends to systems with a mean-field and a chaos generating
two-body interaction (as in nuclei, atoms and diffusive quantum dots). These
developments in many-body quantum chaos are described with special reference to
one-body transition operators.
