  We develop a semi-classical method to simulate the motion of atoms in a
dissipative optical lattice. Our method treats the internal states of the atom
quantum mechanically, including all nonadiabatic couplings, while position and
momentum are treated as classical variables. We test our method in the
one-dimensional case. Excellent agreement with fully quantum mechanical
simulations is found. Our results are much more accurate than those of earlier
semi-classical methods based on the adiabatic approximation.
