Nonstatistical dynamics on the caldera

TL;DR

This paper investigates classical and quantum dynamics in a caldera-shaped potential, revealing a generalized dynamical matching phenomenon where initial conditions influence reaction outcomes, and explores effects of dissipation.

Contribution

It introduces a generalized dynamical matching concept in caldera potentials and compares classical and quantum dynamics, including dissipation effects.

Findings

Classical trajectories confirm dynamical matching at various energies.

Quantum wave packets exhibit a quantum analogue of dynamical matching.

Dissipation influences classical reaction pathways.

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.