MULTIPLICATIVE SEMICLASSICAL DYNAMICS AND THE QUANTIZATION TIME

We study smooth, caustic-free, chaotic semiclassical dynamics on two-d imensional phase space and find that the dynamics can be approached by an iterative procedure that constructs an approximation to the exact long-time semiclassical propagator. semiclassical propagation all the way to the Heisenberg time, where individual eigenstates are resolved, can be computed in polynomial time, obviating the need to sum over an exponentially large number of classical paths. At long times, the dyn amics becomes quantumlike, given by a matrix of the same dimension as the quantum propagator. This matrix, however, differs both from the qu antum and the one-step semiclassical propagators, allowing for the stu dy of the breakdown of the semiclassical approximation. The results sh ed light on the accuracy of the Gutzwiller trace formula in two dimens ions, and on the source of long-time periodic orbit correlations.