The growth of the average kinetic energy of classical particles is studied
for potentials that are random both in space and time. Such potentials are
relevant for recent experiments in optics and in atom optics. It is found that
for small velocities uniform acceleration takes place, and at a later stage
fluctuations of the potential are encountered, resulting in a regime of
anomalous diffusion. This regime was studied in the framework of the
Fokker-Planck approximation. The diffusion coefficient in velocity was
expressed in terms of the average power spectral density, which is the Fourier
transform of the potential correlation function. This enabled to establish a
scaling form for the Fokker-Planck equation and to compute the large and small
velocity limits of the diffusion coefficient. A classification of the random
potentials into universality classes, characterized by the form of the
diffusion coefficient in the limit of large and small velocity, was performed.
It was shown that one dimensional systems exhibit a large variety of novel
universality classes, contrary to systems in higher dimensions, where only one
universality class is possible. The relation to Chirikov resonances, that are
central in the theory of Chaos, was demonstrated. The general theory was
applied and numerically tested for specific physically relevant examples.Comment: 5 pages, 3 figure