Quantum suppression of diffusion on stochastic webs

Quantum suppression of diffusion on stochastic webs is shown to take place for the kicked harmonic oscillator in the form of exactly periodic recurrences. This phenomenon occurs, in general, only if three conditions are satisfied: (1) The kicking potential is odd, up to an additive constant. (2) The web is crystalline with square or hexagonal symmetry. (3) A dimensionless h assumes integer values. The nature of the phenomenon and its sensitivity to small perturbations are examined in terms of generalized kicked Harper models and the theory of topological Chern invariants.