  We study time evolution of a subsystem's density matrix under unitary
evolution, generated by a sufficiently complex, say quantum chaotic,
Hamiltonian, modeled by a random matrix. We exactly calculate all coherences,
purity and fluctuations. We show that the reduced density matrix can be
described in terms of a noncentral correlated Wishart ensemble for which we are
able to perform analytical calculations of the eigenvalue density. Our
description accounts for a transition from an arbitrary initial state towards a
random state at large times, enabling us to determine the convergence time
after which random states are reached. We identify and describe a number of
other interesting features, like a series of collisions between the largest
eigenvalue and the bulk, accompanied by a phase transition in its distribution
function.
