  We derive general evolution equations describing the ensemble-average quantum
dynamics generated by disordered Hamiltonians. The disorder average affects the
coherence of the evolution and can be accounted for by suitably tailored
effective coupling agents and associated rates which encode the specific
statistical properties of the Hamiltonian's eigenvectors and eigenvalues,
respectively. Spectral disorder and isotropically disordered eigenvector
distributions are considered as paradigmatic test cases.
