  Quantized systems whose underlying classical dynamics possess an elaborate
mixture of regular and chaotic motion can exhibit rather subtle long-time
quantum transport phenomena. In a short wavelength regime where semiclassical
theories are most relevant, such transport phenomena, being quintessentially
interference based, are difficult to understand with the system's specific
long-time classical dynamics. Fortunately, semiclassical methods applied to
wave packet propagation can provide a natural approach to understanding the
connections, even though they are known to break down progressively as time
increases. This is due to the fact that some long-time transport properties can
be deduced from intermediate-time behavior. Thus, these methods need only
retain validity and be carried out on much shorter time scales than the
transport phenomena themselves in order to be valuable. The initial value
representation of the semiclassical propagator of Herman and Kluk [M. F. Herman
and E. Kluk, Chem. Phys. 91, 27 (1984)] is heavily used in a number of
molecular and atomic physics contexts, and is of interest here. It is known to
be increasingly challenging to implement as the underlying classical chaos
strengthens, and we ask whether it is possible to implement it well enough to
extract the kind of intermediate time information that reflects wave packet
localization at long times. Using a system of two coupled quartic oscillators,
we focus on the localizing effects of transport barriers formed by stable and
unstable manifolds in the chaotic sea and show that these effects can be
captured with the Herman-Kluk propagator.
