Controlling chaotic scattering: Impulsively driven Morse potential

Lagrangian descriptor and escape time as tools to investigate the dynamics of laser-driven polar molecules

We consider the nonlinear dynamics of a diatomic polar molecule under a linearly polarized laser field. We assume a model in which the molecule dipole is coupled with a time-dependent electric field. This system presents a bound energy region where the atoms are bound, and a free-energy region where the atoms are dissociated. Due to the nonalignment between the dipole axis and the laser direction, and the time dependence of the external field, this system presents two and a half degrees of freedom, namely the vibrational degree, the rotation degree, and the time. To investigate the system dynamics, instead of using the Poincaré surface-of-section technique, we propose the use of the Lagrangian descriptor associated with the escape times. The Lagrangian descriptor is a quantity that reveals complex structures in the phase space, whereas the escape times are the time span in which a trajectory is initially in the bound region before escaping to the unbound region. The combination of these two quantities allows us to distinguish between real stability regions from other complex structures, including stickiness regions, and a different formation, which we call escape islands. With the help of these tools, we find that for high-field amplitudes the inclusion of rotation leads to an increase of the stability regions, which implies a decrease of the dissociation in comparison with the one-dimensional case.

Nonperiodic delay mechanism and fractallike behavior in classical time-dependent scattering

We study the occurrence of delay mechanisms other than periodic orbits in scattering systems with time-dependent potentials. By using as model system two harmonically oscillating disks on a plane, we have found the existence of a mechanism not related to the periodic orbits of the system, that delays trajectories in the scattering region. This mechanism creates a fractallike structure in the scattering functions and can possibly occur in several time-dependent scattering systems.

Chaotic scattering: An introduction

In recent years chaotic behavior in scattering problems has been found to be important in a host of physical situations. Concurrently, a fundamental understanding of the dynamics in these situations has been developed, and such issues as symbolic dynamics, fractal dimension, entropy, and bifurcations have been studied. The quantum manifestations of classical chaotic scattering is also an extremely active field, with new analytical techniques being developed and with experiments being carried out. This issue of Chaos provides an up-to-date survey of the range of work in this important field of study.

Chaotic scattering on a double well: Periodic orbits, symbolic dynamics, and scaling

We investigate classical scattering of particles by a double-well potential. Irregularity in the scattering functions, such as scattering angle and escape time, appears when the collision energy is lowered below a threshold value. This threshold is closely related to the appearance of periodic orbits with energies above the potential maxima. We study the scattering as a function of the energy and impact parameter. In this initial parameter space the scattering functions consist of regular regions interlaced with chaotic rivers. A symbolic dynamics has been developed to organize these structures and used to reveal their scaling properties.

Chaotic electronic scattering with He(+)

We investigate classical electronic collisions with a He(+) ion. Scattering functions, such as the scattering angle, collisional time, or energy of the outgoing electron, all exhibit an interesting hierarchial self-similar structure, which can be interpreted in terms of the indefinite number of electronic returns to the vicinity of the nucleus, encounters between electrons, and Keplerian excursions of electrons during the collisional processes. Based on this mechanism a binary coding is introduced to organize the dynamics of this three-body system and to provide an understanding of the self-similarity among generations of scale magnification, which yields escape rates that vary with the sectional cut into the parameter space. The self-similarity displayed within a single generation, on the other hand, can be simply tied to the periods of the two independent electronic excursions. The physical interpretation and the symbolic dynamics introduced here are generally useful for three-body collisional systems, including atomic, molecular, or stellar collisions.