  The channel induced by a complex system interacting strongly with a qubit is
calculated exactly under the assumption of randomness of its eigenvectors. The
resulting channel is represented as an isotropic time dependent oscillation of
the Bloch ball, leading to non-Markovian behavior, even in the limit of
infinite environments. Two contributions are identified: one due to the density
of states and the other due to correlations in the spectrum. Prototype
examples, one for chaotic and the other for regular dynamics are explored.
