  This paper describes the dynamics of a quantum two-level system (qubit) under
the influence of an environment modeled by an ensemble of random matrices. In
distinction to earlier work, we consider here separable couplings and focus on
a regime where the decoherence time is of the same order of magnitude than the
environmental Heisenberg time. We derive an analytical expression in the linear
response approximation, and study its accuracy by comparison with numerical
simulations. We discuss a series of unusual properties, such as purity
oscillations, strong signatures of spectral correlations (in the environment
Hamiltonian), memory effects and symmetry breaking equilibrium states.
