Pericyclic reactions with energies E well above the potential energy barrier B (case E>B) proceed with quantum nuclear flux densities 〈j〉 which are essentially proportional to the nuclear densities ρ in the femtosecond time domain. This corresponds to the definition of classical (cl) mechanics, jcl=υclρcl, with almost constant velocity vcl. For the other case E<B, however, that is, in the domain of coherent tunneling, we discover the opposite trend, that is, 〈j〉 has maximum value close to the barrier where ρ is a minimum (in fact where ρ is close to zero). The general conclusion is that quantum mechanical nuclear flux densities may be at variance from traditional expectations based on classical trajectories. This prediction calls for experimental demonstration. The counter-intuitive proof-of-principle is demonstrated for a simple, one-dimensional model of the Cope rearrangement of semibullvalene.