Diffusion and localization for the Chirikov typical map.

We consider the classical and quantum properties of the "Chirikov typical map," proposed by Boris Chirikov in 1969. This map is obtained from the well-known Chirikov standard map by introducing a finite-number T of random phase-shift angles. These angles induce a random behavior for small time-scales (t<T) and a T -periodic iterated map which is relevant for larger time-scales (t>T) . We identify the classical chaos border k(c) approximately T (-3/2)1 for the kick parameter k and two regimes with diffusive behavior on short and long time scales. The quantum dynamics is characterized by the effect of Chirikov localization (or dynamical localization). We find that the localization length depends in a subtle way on the two classical diffusion constants in the two time-scale regime.