Quantum-classical correspondence in many-dimensional quantum chaos is investigated by use of a coupled quantum kicked-rotors model. Even when the number of rotors is only two, results obtained are drastically different from those for a single-rotor system; that is, in the semiclassical limit the coupled system restores the essential features of classical chaos under appropriate conditions. In particular, the time-reversal experiment reveals that the classical chaotic mixing is recovered almost entirely; however, the recovered mixing is "conditional" in the sense that there exists a threshold for the recovery.
Questions of how the nature of a reaction coordinate that dominates the reaction ceases to exist and whether some new features emerge as an increase of total energy of systems are investigated for many degrees of freedom Hamiltonian systems. As a model system, a hydrogen atom in crossed electric and magnetic fields is scrutinized. It is shown that, when the total energy increases, the reaction coordinate no longer dominates the reaction as did at the lower energies. In turn, a new reaction coordinate emerges, connecting totally different reactant and product states. Furthermore, depending on which parts of the phase space the system traverses through the saddle, the system nonuniformly experiences the switching of the reaction coordinate leading to the different product state. The universal mechanism of the cessation and the switching of the reaction coordinate at high energy regimes above the saddle is investigated.
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