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.

Destruction and resurgence of the quasiperiodic shearless attractor.

We consider a dissipative version of the standard nontwist map. It is known that nontwist systems may present a robust transport barrier, called shearless curve, that gives rise to an attractor that retains some of its properties when dissipation is introduced. This attractor is known as shearless attractor, and it may be quasiperiodic or chaotic depending on the control parameters. We describe a route for the destruction and resurgence of the quasiperiodic shearless attractor by analyzing the manifolds of the unstable periodic orbits (UPOs) which are fixed points of the map. We show that the shearless attractor is destroyed by a collision with the UPOs and it resurges after the reconnection of the unstable manifolds of different UPOs.

Tunable Fermi acceleration in a nondissipative driven magnetic billiard.

We study the effect of a constant magnetic field on the dynamics of a system that may present Fermi acceleration (FA). The model in consideration is the nondissipative annular billiard with breathing boundaries. There is a field threshold, from which the mechanism of FA can be deactivated. The presence of the magnetic field curves the particle trajectories and for some combinations of the parameters FA is totally, and nontrivially, suppressed without considering any kind of dissipation.

Dissipation as a mechanism of energy gain.

Some properties of the annular billiard under the presence of weak dissipation are studied. We show, in a dissipative system, that the average energy of a particle acquires higher values than its average energy of the conservative case. The creation of attractors, associated with a chaotic dynamics in the conservative regime, both in appropriated regions of the phase space, constitute a generic mechanism to increase the average energy of dynamical systems.

Fluctuations of doublet splittings using the annular billiard.

We study the statistical distribution of quantum energy splittings due to a dynamical tunneling. The system, the annular billiard, has whispering quasimodes due to a discrete symmetry that exists even when chaos is present in the underlying classical dynamics. Symmetric and antisymmetric combinations of these quasimodes correspond to quantum doublet states whose degeneracies decrease as the circles become more eccentric. We construct numerical ensembles composed of splittings for two distinct regimes, one which we call semiclassical for high quantum numbers and high energies where the whispering regions are connected by chaos, and other which we call quantal for low quantum numbers, low energies, and near integrable where dynamical tunneling is not a dominant mechanism. In both cases we observe a variation on the fluctuation amplitudes, but their mean behaviors follow the formula of Leyvraz and Ullmo [J. Phys. A 29, 2529 (1996)]. A description of a three-level collision involving a doublet and a singlet is also provided through a numerical example.