  We study the dynamics of a one-dimensional classical particle in a space and
time dependent potential with randomly chosen parameters. The focus of this
work is a quasi-periodic potential, which only includes a finite number of
Fourier components. The momentum is calculated analytically for short time
within a self-consistent approximation, under certain conditions.
  We find that the dynamics can be described by a model of a random walk
between the Chirikov resonances, which are resonances between the particle
momentum and the Fourier components of the potential. We use numerical methods
to test these results and to evaluate the important properties, such as the
characteristic hopping time between the resonances. This work sheds light on
the short time dynamics induced by potentials which are relevant for optics and
atom optics.
