# Browsing by Subject "chaos"

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Item Arnold diffusion in a driven optical lattice(2016-03) Boretz, Yingyue; Reichl, L. E.; Boretz, Yingyue; Reichl, L. E.Show more The effect of time-periodic forces on matter has been a topic of growing interest since the advent of lasers. It is known that dynamical systems with 2.5 or more degrees of freedom are intrinsically unstable. As a consequence, time-periodic driven systems can experience large excursions in energy. We analyze the classical and quantum dynamics of rubidium atoms confined to a time-periodic optical lattice with 2.5 degrees of freedom. When the laser polarizations are orthogonal, the system consists of two 1.5 uncoupled dynamical systems. When laser polarizations are turned away from orthogonal, an Arnold web forms and the dynamics undergoes a fundamental change. For parallel polarizations, we find huge random excursions in the rubidium atom energies and significant entanglement of energies in the quantum dynamics.Show more Item Chaotic scattering in a molecular system(2009-02) Barr, Alex M.; Na, Kyungsun; Reichl, L. E.; Jung, Christof; Barr, Alex M.; Na, Kyungsun; Reichl, L. E.Show more We study the classical dynamics of bound state and scattering trajectories of the chlorine atom interacting with the HO molecule using a two-dimensional model in which the HO bond length is held fixed. The bound state system forms the HOCl molecule and at low energies is predominantly integrable. Below dissociation a number of bifurcations are observed, most notably a series of saddle-center bifurcations related to a 2:1 and at higher energies 3:1 resonance between bend and stretch motions. At energies above dissociation the classical phase space becomes dominated by a homoclinic tangle which induces a fractal distribution of singularities in all scattering functions. The structure of the homoclinic tangle is examined directly using Poincare surfaces of section as well as indirectly through its influence on the time delay of the scattered chlorine atom and the angular momentum of the scattered HO molecule.Show more Item Classical and Quantum Dynamics of 2D Optical Lattices(2014) Horsley, Eric; Reichl, LindaShow more Here we present the work and results of studies on a two-dimensional optical lattice. The initial work on the classical dynamics describes the onset of chaos using action-angle variables and techniques developed by Walker and Ford \cite{Walker}. Having documented the classical transition to chaos, using a technique called the discrete variable representation, we calculate the eigenvalues and eigenvectors of the two-dimensional optical lattice Hamiltonian operator. The surprising fidelity of these numerical results to the true values (which can be verified for a certain parameter value) will hopefully allow for the future study of level repulsion and the development of quantum phase space distributions (e.g. the Wigner and Husimi quasi-probability distributions).Show more