In this paper, we analyse the phase space structure of the roaming dynamics in a two degree of freedom potential energy surface consisting of two identical planar Morse potentials separated by a distance. This potential energy surface was previously studied in [1], and it has two potential wells surrounded by an unbounded flat region containing no critical points. We study the phase space mechanism for the transference between the wells using the method of Lagrangian descriptors.
We treat a chaotic Hamiltonian scattering system with three degrees of freedom where the chaotic invariant set is of low dimension. Then the chaos and its structure are not visible in scattering functions plotted along one-dimensional lines in the set of asymptotic initial conditions. We show that an asymptotic observer can nevertheless see the structure of the chaotic set in an appropriate scattering function on the two-dimensional impact parameter plane and in the doubly differential cross section. Rainbow singularities in the cross section carry over the symbolic dynamics of the chaotic set into the cross section. A smooth image of the fractal structure of the chaotic set can be reconstructed on the domain of the cross section.
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 [1]. 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 S0 = q f q i p • dq.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.