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

Abstract

We study the phase space objects 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 this model, two features determine the evolution of the system: a Van der Waals force and a short-range force associated with the many-body interactions. In the previous work, small random periodic changes in the direction of the momentum were used 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 to simulate the short-range effects between the particles in the system. We compare both variants of the model and explain their differences and similarities from a phase space perspective. 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}=∫_{q_{i}}^{q_{f}}p·dq.