Fractal scattering dynamics of the three-dimensional HOCl molecule

Lin, Yi Der; Barr, Alex M.; Reichl, L. E.; Jung, Christof

doi:10.1103/physreve.87.012917

Cited by 10 publications

(7 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The present system helps to clarify the elementary transitions in the scattering functions and the corresponding transitions in the cross-section in other systems with qualitatively similar changes in the scattering function, for example 3-dof systems with a perturbation of partial integrability [11], [12], [35], a perturbed magnetic dipole [14], and a realistic molecular system treated in [36]. The considerations of subsections 3.1 and 3.3 hold for all the above mentioned system in an analogous form.…”

Section: Remarks and Conclusionmentioning

confidence: 89%

Atom scattering off a vibrating surface: An example of chaotic scattering with three degrees of freedom

González¹,

Borondo²,

Jung³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

In this article, we study the classical chaotic scattering of a He atom off a harmonically vibrating Cu surface. The three degrees of freedom (3dof) model is studied by first considering the non-vibrating 2-dof model for different values of the energy. We calculate the set of singularities of the scattering functions and study its connection with the tangle between the stable and unstable manifolds of the fixed point at an infinite distance to the Cu surface in the Poincaré map for different values of the initial energy. With these manifolds, it is possible to construct the stable and unstable manifolds for the 3-dof coupled model considering the extra closed degree of freedom and the deformation of a stack of maps of the 2-dof system calculated at different values of the energy. Also, for the 3-dof system, the resulting invariant manifolds have the correct dimension to divide the constant total energy manifold. By this construction, it is possible to understand the chaotic scattering phenomena for the 3-dof system from a geometric point of view. We explain the connection between the set of singularities of the scattering function, the Jacobian determinant of the scattering function, the relevant invariant manifolds in the scattering problem, and the cross-section, as well as their behavior when the coupling due to the surface vibration is switched on. In particular, we present in detail the connection between the changes in the structure of the caustics in the cross-section and the changes in the zero level set of the Jacobian determinant of the scattering function.

show abstract

Section: Remarks and Conclusionmentioning

confidence: 89%

Atom scattering off a vibrating surface: An example of chaotic scattering with three degrees of freedom

González¹,

Borondo²,

Jung³

2019

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Chaotic scattering in open Hamiltonian systems is a fundamental part of the theoretical study of dynamical systems. There are many applications in numerous fields of physics, such as the interaction between the solar wind and the magnetosphere tail [1], the simulation in several dimensions of the molecular dynamics [2], the modeling of chaotic advection of particles in fluid mechanics [3], or the analysis of the escaping mechanism from a star cluster or a galaxy [4,5], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Transient chaos under coordinate transformations in relativistic systems

Fernández,

López,

Seoane

et al. 2020

Preprint

View full text Add to dashboard Cite

We use the Hénon-Heiles system as a paradigmatic model for chaotic scattering to study the Lorentz factor effects on its transient chaotic dynamics. In particular, we focus on how time dilation occurs within the scattering region by measuring the time in a non-inertial clock comoving with the particle. We observe that the several events of time dilation that the particle undergoes exhibit sensitivity to initial conditions. However, the structure of the singularities appearing in the escape time function remains invariant under coordinate transformations. This occurs because the singularities are closely related to the chaotic saddle, which is a time measure independent set. Using a Cantor set approach, we show that the fractal dimension of the escape time function is relativistic invariant. Finally, we relate the fractality in phase space to the unpredictability of the particle final destination. In order to quantify this fractality, we compute the fractal dimensions of the escape time functions as measured with inertial and non-inertial clocks, by means of the uncertainty dimension algorithm. We conclude that, from a mathematical point of view, chaotic transient phenomena are equally predictable in the proper and the inertial reference frames and that transient chaos is coordinate invariant.

show abstract

“…Both fixed points are the source of stable and unstable manifolds that, above dissociation, impart the classical Cl-HO scattering dynamics a fractal structure [18]. The unstable (stable) manifolds, as they evolve forward (backward) in time, form a fractal network of tendrils that define the chaotic region of the phase space (see Appendix A).…”

Section: Periodic Orbits Of Hoclmentioning

confidence: 99%

“…5.2.a. The trajectories are caught up in the fractal structure of tangles in the chaotic region [14,18], and cycle around the chaotic layer until they eventually escape into the asymptotic region as the molecule dissociates. In Fig.…”

Section: Periodic Orbits Of Hoclmentioning

confidence: 99%

See 1 more Smart Citation

The vibrational dynamics of 3D HOCl above dissociation

Lin

Reichl

Jung

2015

The Journal of Chemical Physics

Self Cite

View full text Add to dashboard Cite

We explore the classical vibrational dynamics of the HOCl molecule for energies above the dissociation energy of the molecule. Above dissociation, we find that the classical dynamics is dominated by an invariant manifold which appears to stabilize two periodic orbits at energies significantly above the dissociation energy. These stable periodic orbits can hold a large number of quantum states and likely can support a significant quasibound state of the molecule, well above the dissociation energy. The classical dynamics and the lifetime of quantum states on the invariant manifold are determined.

show abstract

Fractal scattering dynamics of the three-dimensional HOCl molecule

Cited by 10 publications

References 16 publications

Atom scattering off a vibrating surface: An example of chaotic scattering with three degrees of freedom

Atom scattering off a vibrating surface: An example of chaotic scattering with three degrees of freedom

Transient chaos under coordinate transformations in relativistic systems

The vibrational dynamics of 3D HOCl above dissociation

Contact Info

Product

Resources

About