Phase Space Structure and Transport in a Caldera Potential Energy Surface

Abstract

We study phase space transport in a 2D caldera potential energy surface (PES) using techniques from nonlinear dynamics. The caldera PES is characterized by a flat region or shallow minimum at its center surrounded by potential walls and multiple symmetry related index one saddle points that allow entrance and exit from this intermediate region.We have discovered four qualitatively distinct cases of the structure of the phase space that govern phase space transport. These cases are categorized according to the total energy and the stability of the periodic orbits associated with the family of the central minimum, the bifurcations of the same family, and the energetic accessibility of the index one saddles. In each case we have computed the invariant manifolds of the unstable periodic orbits of the central region of the potential and the invariant manifolds of the unstable periodic orbits of the families of periodic orbits associated with the index one saddles. We have found that there are three distinct mechanisms determined by the invariant manifold structure of the unstable periodic orbits govern the phase space transport. The first mechanism explains the nature of the entrance of the trajectories from the region of the low energy saddles into the caldera and how they may become trapped in the central region of the potential. The second mechanism describes the trapping of the trajectories that begin from the central region of the caldera, their transport to the regions of the saddles, and the nature of their exit from the caldera. The third mechanism describes the phase space geometry responsible for the dynamical matching of trajectories originally proposed by Carpenter and described in Collins et al. (2014) for the two dimensional caldera PES that we consider.

24 pages, International Journal of Bifurcation and Chaos (in press)

References in corpus (2)

• Nonstatistical dynamics on the caldera
• Dynamics on the Double Morse Potential: A Paradigm for Roaming Reactions with no Saddle Points

Cited by in corpus (11)

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• Detection of Dynamical Matching in a Caldera Hamiltonian System using Lagrangian Descriptors
• Phase Space Analysis of the Non-Existence of Dynamical Matching in a Stretched Caldera Potential Energy Surface
• The Dynamical Matching Mechanism in Phase Space for Caldera-Type Potential Energy Surfaces
• The Nature of Reactive and Non-reactive Trajectories for a Three Dimensional Caldera Potential Energy Surface
• The bifurcations of the critical points and the role of the depth in a symmetric Caldera potential energy surface
• The Influence of a Pitchfork Bifurcation of the Critical Points of a Symmetric Caldera Potential Energy Surface on Dynamical Matching
• Phase space transport in a symmetric Caldera potential with three index-1 saddles and no minima
• Bifurcation of Dividing Surfaces Constructed from Period-Doubling Bifurcations of Periodic Orbits in a Caldera Potential Energy Surface
• From Poincare Maps to Lagrangian Descriptors: The Case of the Valley Ridge Inflection Point Potential
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