  A semiclassical theory of chaotic atomic transport in a one-dimensional
nondissipative optical lattice is developed. Using the basic equations of
motion for the Bloch and translational atomic variables, we derive a stochastic
map for the synchronized component of the atomic dipole moment that determines
the center-of-mass motion. We find the analytical relations between the atomic
and lattice parameters under which atoms typically alternate between flying
through the lattice and being trapped in the wells of the optical potential. We
use the stochastic map to derive formulas for the probability density functions
(PDFs) for the flight and trapping events. Statistical properties of chaotic
atomic transport strongly depend on the relations between the atomic and
lattice parameters. We show that there is a good quantitative agreement between
the analytical PDFs and those computed with the stochastic map and the basic
equations of motion for different ranges of the parameters. Typical flight and
trapping PDFs are shown to be broad distributions with power law ``heads'' with
the slope -1.5 and exponential ``tails''. The lengths of the power law and
exponential parts of the PDFs depend on the values of the parameters and can be
varied continuously. We find analytical conditions, under which deterministic
atomic transport has fractal properties, and explain a hierarchical structure
of the dynamical fractals.
