  Dissipation and decoherence, and the evolution from pure to mixed states in
quantum physics are handled through master equations for the density matrix. By
embedding elements of this matrix in a higher-dimensional Liouville-Bloch
equation, the methods of unitary integration are adapted to solve for the
density matrix as a function of time, including the non-unitary effects of
dissipation and decoherence. The input requires only solutions of classical,
initial value time-dependent equations. Results are illustrated for a damped
driven two-level system.
