Chaos and thermalization in a classical chain of dipoles.

We explore the connection between chaos, thermalization, and ergodicity in a linear chain of N interacting dipoles. Starting from the ground state, and considering chains of different numbers of dipoles, we introduce single site excitations with excess energy ΔK. The time evolution of the chaoticity of the system and the energy localization along the chain is analyzed by computing, up to a very long time, the statistical average of the finite-time Lyapunov exponent λ(t) and the participation ratio Π(t). For small ΔK, the evolution of λ(t) and Π(t) indicates that the system becomes chaotic at approximately the same time as Π(t) reaches a steady state. For the largest considered values of ΔK the system becomes chaotic at an extremely early stage in comparison with the energy relaxation times. We find that this fact is due to the presence of chaotic breathers that keep the system far from equipartition and ergodicity. Finally, we show numerically and analytically that the asymptotic values attained by the participation ratio Π(t) fairly correspond to thermal equilibrium.

Energy transfer mechanisms in a dipole chain: From energy equipartition to the formation of breathers.

We study the energy transfer in a classical dipole chain of N interacting rigid rotating dipoles. The underlying high-dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their stability in the common plane of rotation. Starting from the minimal energy configuration, the response of the chain to excitation of a single dipole is investigated. Using both the linearized and the exact Hamiltonian of the dipole chain, we detect an approximate excitation energy threshold between a weakly and a strongly nonlinear dynamics. In the weakly nonlinear regime, the chain approaches in the course of time the expected energy equipartition among the dipoles. For excitations of higher energy, strongly localized excitations appear whose trajectories in time are either periodic or irregular, relating to the well-known discrete or chaotic breathers, respectively. The phenomenon of spontaneous formation of domains of opposite polarization and phase locking is found to commonly accompany the time evolution of the chaotic breathers. Finally, the sensitivity of the dipole chain dynamics to the initial conditions is studied as a function of the initial excitation energy by computing a fast chaos indicator. The results of this study confirm the aforementioned approximate threshold value for the initial excitation energy, below which the dynamics of the dipole chain is regular and above which it is chaotic.

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.

Nonlinear dynamics of atoms in a crossed optical dipole trap.

We explore the classical dynamics of atoms in an optical dipole trap formed by two identical Gaussian beams propagating in perpendicular directions. The phase space is a mixture of regular and chaotic orbits, the latter becoming dominant as the energy of the atoms increases. The trapping capabilities of these perpendicular Gaussian beams are investigated by considering an atomic ensemble in free motion. After a sudden turn on of the dipole trap, a certain fraction of atoms in the ensemble remains trapped. The majority of these trapped atoms has energies larger than the escape channels, which can be explained by the existence of regular and chaotic orbits with very long escape times.

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.

Octupolar perturbation of a single ion in a Penning trap.

We investigate the classical dynamics of a single ion trapped in a Penning trap perturbed by a octupolar electrostatic perturbation that introduces nonlinearities in the motion. We show that the dynamics is controlled by a single external parameter that combines the influence of the electric and magnetic fields. Through the variation of this parameter, we explore the evolution of the phase space structure of the system by the numerical continuation of the families of periodic orbits.