  We investigate the transport of particles in the chaotic component of phase
space for a two-dimensional, area-preserving nontwist map. The survival
probability for particles within the chaotic sea is described by an exponential
decay for regions in phase space predominantly chaotic and it is scaling
invariant in this case. Alternatively, when considering mixed chaotic and
regular regions, there is a deviation from the exponential decay, characterized
by a power law tail for long times, a signature of the stickiness effect.
Furthermore, due to the asymmetry of the chaotic component of phase space with
respect to the line $I = 0$, there is an unbalanced stickiness which generates
a ratchet current in phase space. Finally, we perform a phenomenological
description of the diffusion of chaotic particles by identifying three scaling
hypotheses, and obtaining the critical exponents via extensive numerical
simulations.
