  We derive an elegant solution for a two-level system evolving adiabatically
under the influence of a driving field with a time-dependent phase, which
includes open system effects such as dephasing and spontaneous emission. This
solution, which is obtained by working in the representation corresponding to
the eigenstates of the time-dependent Hermitian Hamiltonian, enables the
dynamic and geometric phases of the evolving density matrix to be separated and
relatively easily calculated.
