J. Pablo Salas

Bifurcations of dividing surfaces in chemical reactions.

We study the dynamical behavior of the unstable periodic orbit (NHIM) associated to the non-return transition state (TS) of the H(2) + H collinear exchange reaction and their effects on the reaction probability. By means of the normal form of the Hamiltonian in the vicinity of the phase space saddle point, we obtain explicit expressions of the dynamical structures that rule the reaction. Taking advantage of the straightforward identification of the TS in normal form coordinates, we calculate the reaction probability as a function of the system energy in a more efficient way than the standard Monte Carlo method. The reaction probability values computed by both methods are not in agreement for high energies. We study by numerical continuation the bifurcations experienced by the NHIM as the energy increases. We find that the occurrence of new periodic orbits emanated from these bifurcations prevents the existence of a unique non-return TS, so that for high energies, the transition state theory cannot be longer applied to calculate the reaction probability.

Dynamics of a single ion in a perturbed Penning trap: Octupolar perturbation

Imperfections in the design or implementation of Penning traps may give rise to electrostatic perturbations that introduce nonlinearities in the dynamics. In this paper we investigate, from the point of view of classical mechanics, the dynamics of a single ion trapped in a Penning trap perturbed by an octupolar perturbation. Because of the axial symmetry of the problem, the system has two degrees of freedom. Hence, this model is ideal to be managed by numerical techniques like continuation of families of periodic orbits and Poincaré surfaces of section. We find that, through the variation of the two parameters controlling the dynamics, several periodic orbits emanate from two fundamental periodic orbits. This process produces important changes (bifurcations) in the phase space structure leading to chaotic behavior.

Rydberg hydrogen atom near a metallic surface : Stark regime and ionization dynamics

We investigate the classical dynamics of a hydrogen atom near a metallic surface in the presence of a uniform electric field. To describe the atom-surface interaction we use a simple electrostatic image model. Owing to the axial symmetry of the system, the z-component of the canonical angular momentum P{sub {phi}} is an integral and the electronic dynamics is modeled by a two degrees of freedom Hamiltonian in cylindrical coordinates. The structure and evolution of the phase space as a function of the electric field strength is explored extensively by means of numerical techniques of continuation of families of periodic orbits and Poincare surfaces of section. We find that, due to the presence of the electric field, the atom is strongly polarized through two consecutive pitchfork bifurcations that strongly change the phase space structure. Finally, by means of the phase space transition state theory and the classical spectral theorem, the ionization dynamics of the atom is studied.

Analysis of the classical phase space and energy transfer for two rotating dipoles with and without external electric field

We explore the classical dynamics of two interacting rotating dipoles that are fixed in the space and exposed to an external homogeneous electric field. Kinetic energy transfer mechanisms between the dipoles are investigated by varying both the amount of initial excess kinetic energy of one of them and the strength of the electric field. In the field-free case, and depending on the initial excess energy, an abrupt transition between equipartition and nonequipartition regimes is encountered. The study of the phase space structure of the system as well as the formulation of the Hamiltonian in an appropriate coordinate frame provide a thorough understanding of this sharp transition. When the electric field is turned on, the kinetic energy transfer mechanism is significantly more complex and the system goes through different regimes of equipartition and nonequipartition of the energy including chaotic behavior.

Driving the formation of the RbCs dimer by a laser pulse: A nonlinear-dynamics approach

We study the formation of the RbCs molecule by an intense laser pulse using nonlinear dynamics. Under the Born-Oppenheimer approximation, the system is modeled by a two degree of freedom rovibrational Hamiltonian, which includes the ground electronic potential energy curve of the diatomic molecule and the interaction of the molecular polarizability with the electric field of the laser. As the laser intensity increases, we observe that the formation probability first increases and then decreases after reaching a maximum. We show that the analysis can be simplified to the investigation of the long-range interaction between the two atoms. We conclude that the formation is due to a very small change in the radial momentum of the dimer induced by the laser pulse. From this observation, we build a reduced one dimensional model which allows us to derive an approximate expression of the formation probability as a function of the laser intensity.