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The growth of the average kinetic energy of classical particles is studiedfor potentials that are random both in space and time. Such potentials arerelevant for recent experiments in optics and in atom optics. It is found thatfor small velocities uniform acceleration takes place, and at a later stagefluctuations of the potential are encountered, resulting in a regime ofanomalous diffusion. This regime was studied in the framework of theFokker-Planck approximation. The diffusion coefficient in velocity wasexpressed in terms of the average power spectral density, which is the Fouriertransform of the potential correlation function. This enabled to establish ascaling form for the Fokker-Planck equation and to compute the large and smallvelocity limits of the diffusion coefficient. A classification of the randompotentials into universality classes, characterized by the form of thediffusion coefficient in the limit of large and small velocity, was performed.It was shown that one dimensional systems exhibit a large variety of noveluniversality classes, contrary to systems in higher dimensions, where only oneuniversality class is possible. The relation to Chirikov resonances, that arecentral in the theory of Chaos, was demonstrated. The general theory wasapplied and numerically tested for specific physically relevant examples.

Is transport in time-dependent random potentials universal ?