Semiclassical dynamical localization and the multiplicative   semiclassical propagator
  We describe an iterative approach to computing long-time semiclassical dynamics in the presence of chaos, which eliminates the need for summing over an exponentially large number of classical paths, and has good convergence properties even beyond the Heisenberg time. Long-time semiclassical properties can be compared with those of the full quantum system. The method is used to demonstrate semiclassical dynamical localization in one-dimensional classically diffusive systems, showing that interference between classical paths is a sufficient mechanism for limiting long-time phase space exploration. 
L. Kaplan