  We study the quantum dissipative Duffing oscillator across a range of system
sizes and environmental couplings under varying semiclassical approximations.
Using spatial (based on Kullback-Leibler distances between phase-space
attractors) and temporal (Lyapunov exponent-based) complexity metrics, we
isolate the effect of the environment on quantum-classical differences.
Moreover, we quantify the system sizes where quantum dynamics cannot be
simulated using semiclassical or noise-added classical approximations.
Remarkably, we find that a parametrically invariant meta-attractor emerges at a
specific length scale and noise-added classical models deviate strongly from
quantum dynamics below this scale. Our findings also generalize the previous
surprising result that classically regular orbits can have the greatest
quantum-classical differences in the semiclassical regime. In particular, we
show that the dynamical growth of quantum-classical differences is not
determined by the degree of classical chaos.
