Quantum tunneling through classical chaos
Y. Karni and E.E. Nikitin
Department of Chemistry, Technion, Haifa 32000, Israel
and Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia
We have made a comparative study of quantum and classical dynamics of a system
that simulates either the vibrational predissociation of a van der Waals
triatomic complex or the photodissociation of a diatomic molecule under the
action of high-frequency radiation [1]. For our model, the quantum mechanical
dissociation rate, calculated both by the accurate complex-scaling method [2]
and by the Landau adiabatic perturbation theory [3], never becomes comparable to the
classical dissociation rate. The latter either vanishes when the initial excitation
energy of the dissociating oscillator is low (regular regime) or rapidly
increases with energy (chaotic regime). The nonzero rate for the quantum
dynamics at low energies is interpreted as tunneling. The lower rate for
quantum dynamics at high energies (compared to that for classical dynamics)
is related to the property of the phase space: in a chaotic regime, the classical
system escapes to the dissociation continuum through the holes which are too narrow
for a passage of a quantal object of finite action dimension 
.
Therefore, a system still has to tunnel through the classical chaos.