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Quantized systems whose underlying classical dynamics possess an elaboratemixture of regular and chaotic motion can exhibit rather subtle long-timequantum transport phenomena. In a short wavelength regime where semiclassicaltheories are most relevant, such transport phenomena, being quintessentiallyinterference based, are difficult to understand with the system's specificlong-time classical dynamics. Fortunately, semiclassical methods applied towave packet propagation can provide a natural approach to understanding theconnections, even though they are known to break down progressively as timeincreases. This is due to the fact that some long-time transport properties canbe deduced from intermediate-time behavior. Thus, these methods need onlyretain validity and be carried out on much shorter time scales than thetransport phenomena themselves in order to be valuable. The initial valuerepresentation of the semiclassical propagator of Herman and Kluk [M. F. Hermanand E. Kluk, Chem. Phys. 91, 27 (1984)] is heavily used in a number ofmolecular and atomic physics contexts, and is of interest here. It is known tobe increasingly challenging to implement as the underlying classical chaosstrengthens, and we ask whether it is possible to implement it well enough toextract the kind of intermediate time information that reflects wave packetlocalization at long times. Using a system of two coupled quartic oscillators,we focus on the localizing effects of transport barriers formed by stable andunstable manifolds in the chaotic sea and show that these effects can becaptured with the Herman-Kluk propagator.

Investigating quantum transport with an initial value representation of the semiclassical propagator