A nonadiabatic semi-classical method for dynamics of atoms in optical   lattices
  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. 
S. Jonsell, C. M. Dion, M. Nyl\'en, S. J. H. Petra, P. Sj\"olund, A.   Kastberg