Nonstandard diffusion properties of the standard map

The diffusion properties of the Chirikov-Taylor standard map are shown to be nonuniversal in the framework of the wave-particle interaction, because this map corresponds to a spectrum of waves whose initial phases are all correlated. The occurrence of diffusion is shown to be a peculiarity of the standard map when the average is made over the particles' initial positions. The force correlation time is shown to decrease more slowly with the wave amplitudes for the standard map than for waves with noncorrelated phases. Levy flights are shown to be one more peculiarity of the standard map.