Chaotic dynamics in multidimensional transition states
journal contributionposted on 10.09.2014, 10:54 by Ali Allahem, Thomas BartschThomas Bartsch
The crossing of a transition state in a multidimensional reactive system is mediated by invariantgeometric objects in phase space: An invariant hyper-sphere that represents the transition stateitself and invariant hyper-cylinders that channel the system towards and away from the transitionstate. The existence of these structures can only be guaranteed if the invariant hyper-sphere isnormally hyperbolic, i.e., the dynamics within the transition state is not too strongly chaotic. We study thedynamics within thetransition state for the hydrogen exchangereaction in three degrees of freedom. As the energy increases, the dynamics within the transition statebecomes increasingly chaotic. We find that the transition state first looses and then, surprisingly,regains its normal hyperbolicity. The important phase space structures of transition state theory will, therefore,exist at most energies above the threshold.
The first author is supported by Qassim University and the Ministry of Higher Education of Saudi Arabia. The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union's Seventh Framework Programme FP7/2007-2013/ under REA Grant Agreement No. 294974.
- Mathematical Sciences