Phase space structure and escape time dynamics in a Van der Waals model for exothermic reactions

TL;DR

This paper investigates phase space structures influencing transport and escape times in a Hamiltonian model of ultracold exothermic reactions, comparing different short-range interaction simulations.

Contribution

It introduces a new phase space analysis of a Van der Waals model with Gaussian bumps, enhancing understanding of reaction dynamics and transport mechanisms.

Findings

Comparison of random periodic and Gaussian bump models reveals key differences in phase space structures.

Construction of a Lagrangian descriptor based on Maupertuis action visualizes dynamical structures.

Insights into how short-range interactions affect reaction yield and escape times.

Abstract

We study the phase space structures that control the transport in a classical Hamiltonian model for a chemical reaction. This model has been proposed to study the yield of products in an ultracold exothermic reaction. In the considered model, two elements determine the evolution of the system: a Van der Waals force and short-range force associated with the many-body interactions. In the previous work has been used small random periodic changes in the direction of the momentum to simulate the short-range many-body interactions. In the present work, random Gaussian bumps have been added to the Van der Waals potential energy simulate the short-range effects between the particles in the system. We compare both variants of the model and explain their differences similarities and differences from a phase space perspective. In order to visualize the structures that direct the dynamics in the phase space, we construct a natural Lagrangian descriptor for Hamiltonian systems based on the Maupertuis action $S_0$.