موجز عن البحث:
The crossing of a transition state in a
multidimensional reactive system is mediated by invariant geometric objects
in phase space: An invariant hyper-sphere that represents the transition
state itself and invariant hyper-cylinders that channel the system towards
and away from the transition state. The existence of these structures can
only be guaranteed if the invariant hyper-sphere is normally hyperbolic,
i.e., the dynamics within the transition state is not too strongly chaotic.
We study the dynamics within the transition state for the hydrogen exchange
reaction in three degrees of freedom. As the energy increases, the dynamics
within the transition state becomes 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.
موجز عن المشاركة
reactions can be described as the crossing of an energetic barrier. This
process is mediated by an invariant object in phase space. One can construct
a normally hyperbolic invariant manifold (NHIM) of the reactive dynamical
system that can be considered as the geometric representation of the transition
state itself. It is an invariant sphere. The NHIM has invariant cylinders
(reaction channels) attached to it. This invariant geometric structure
survives as long as the invariant sphere is normally hyperbolic. We applied
this theory to the hydrogen exchange reaction in three degrees of freedom.
above the reaction threshold, the dynamics within the
transition state becomes partially chaotic. We have found that the invariant
sphere first ceases to be normally hyperbolic at fairly low energies.
Surprisingly normal hyperbolicity is then restored and the invariant sphere
remains normally hyperbolic even at very high energies.