Semiclassical propagation: How long can it last?

Abstract

The Van Vleck–Gutzwiller propagator is a fundamental quantity in semiclassical theory whose validity was recently demonstrated to extend beyond the time previously thought feasible, i.e., well past the time after which classical chaos has mixed the phase space on a scale smaller than Plancks’s constant. Little justification was given for this seeming contradiction of the usual vision of semiclassical errors. Though perhaps nonintuitive, we find that standard arguments, properly applied to chaotic dynamics, do explain the long time accuracy.