  A model is investigated where a monochromatic, spatially homogeneous laser
field interacts with an electron in a one-dimensional periodic lattice. The
classical Hamiltonian is presented and the technique of stroboscopic maps is
used to study the dynamical behavior of the model. The electron motion is found
to be completely regular only for small field amplitudes, developing a larger
chaotic region as the amplitude increases. The quantum counterpart of the
classical Hamiltonian is derived. Exact numerical diagonalizations show the
existence of universal, random-matrix fluctuations in the electronic energy
bands dressed by the laser field. A detailed analysis of the classical phase
space is compatible with the statistical spectral analysis of the quantum
model. The application of this model to describe transport and optical
absorption in semiconductor superlattices submitted to intense infrared laser
radiation is proposed.
