  We study dissipative transport of spontaneously emitting atoms in a 1D
standing-wave laser field in the regimes where the underlying deterministic
Hamiltonian dynamics is regular and chaotic. A Monte Carlo stochastic
wavefunction method is applied to simulate semiclassically the atomic dynamics
with coupled internal and translational degrees of freedom. It is shown in
numerical experiments and confirmed analytically that chaotic atomic transport
can take the form either of ballistic motion or a random walking with specific
statistical properties. The character of spatial and momentum diffusion in the
ballistic atomic transport is shown to change abruptly in the atom-laser
detuning regime where the Hamiltonian dynamics is irregular in the sense of
dynamical chaos. We find a clear correlation between the behavior of the
momentum diffusion coefficient and Hamiltonian chaos probability which is a
manifestation of chaoticity of the fundamental atom-light interaction in the
diffusive-like dissipative atomic transport. We propose to measure a linear
extent of atomic clouds in a 1D optical lattice and predict that, beginning
with those values of the mean cloud's momentum for which the probability of
Hamiltonian chaos is close to 1, the linear extent of the corresponding clouds
should increase sharply. A sensitive dependence of statistical characteristics
of dissipative transport on the values of the detuning allows to manipulate the
atomic transport by changing the laser frequency.
