Nonstatistical dynamics on the caldera

Abstract

We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles associated with entrance/exit channels. Classical trajectory simulations at several different energies confirm the existence of the `dynamical matching' phenomenon originally proposed by Carpenter, where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction (passage through the diametrically opposing exit channel). By studying a `stretched' version of the caldera model, we have uncovered a generalized dynamical matching: bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point. We also investigate the effects of dissipation on the classical dynamics. In addition to classical trajectory studies, we examine the dynamics of quantum wave packets on the caldera potential (stretched and unstretched). These computations reveal a quantum mechanical analogue of the `dynamical matching' phenomenon, where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product.

54 pages, 17 figures

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Cited by in corpus (11)

• Detection of Dynamical Matching in a Caldera Hamiltonian System using Lagrangian Descriptors
• Phase Space Structure and Transport in a Caldera Potential Energy Surface
• 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
• Influence of low frequency modes on dynamical concertedness in double proton transfer dynamics
• Low-Dimensional Projection of Reactive Islands in Chemical Reaction Dynamics Using a Supervised Dimensionality Reduction Method
• Revealing the phase space structure of Hamiltonian systems using the action