Escape of trajectories from a vase-shaped cavity

Classical Fractals and Quantum Chaos in Ultracold Dipolar Collisions

We examine a dipolar-gas model to address fundamental issues regarding the correspondence between classical chaos and quantum observations in ultracold dipolar collisions. The theoretical model consists of a short-range Lennard-Jones potential well with an anisotropic, long-range dipole-dipole interaction between two atoms. Both the classical and quantum dynamics are explored for the same Hamiltonian of the system. The classical chaotic scattering is revealed by the fractals developed in the scattering function (defined as the final atom separation as a function of initial conditions), while the quantum chaotic features lead to the repulsion of the eigenphases from the corresponding quantum S matrix. The nearest-eigenphase-spacing statistics have an intermediate behavior between the Poisson and the Wigner-Dyson distributions. The character of the distribution can be controlled by changing an effective Planck constant or the dipole moment. The degree of quantum chaos shows a good correspondence with the overall average of the classical scattering function. The results presented here also provide helpful insights for understanding the role of the inherent dipole-dipole interaction in the currently ongoing experiments on ultracold collisions of highly magnetic atoms.

Photodetached electron spectrum of H- near a surface having spherical dent

The detached electron flux and photodetachment cross section are derived using the theoretical imaging method and quantum approach for system comprising of hydrogen negative ion ([Formula: see text]) placed near a surface having spherical dent. The dent is modeled like a spherical concave surface. It is observed that the spherical dent generates additional oscillatory and smooth structure in the detached electron flux and photodetachment cross section, respectively. The radius of curvature, inter-ion surface distance and the dent factor strongly manipulate the results. When the inter-ion surface distance is equal to the focal length of the concave surface, the detached electron flux and photodetachment cross section are not well behaved. The photodetachment cross section is also not well behaved for the inter-ion surface distance equal to the radius of curvature. The focus and center of curvature of the concave surface act as a spherical singularity. This study gives new understanding on the photodetachment of negative ions in the vicinity of concave surfaces.

Topological analysis of chaotic transport through a ballistic atom pump

We examine a system consisting of two reservoirs of particles connected by a channel. In the channel are two oscillating repulsive potential-energy barriers. It is known that such a system can transport particles from one reservoir to the other, even when the chemical potentials in the reservoirs are equal. We use computations and the theory of chaotic transport to study this system. Chaotic transport is described by passage around or through a heteroclinic tangle. Topological properties of the tangle are described using a generalization of homotopic lobe dynamics, which is a theory that gives some properties of intermediate-time behavior from properties of short-time behavior. We compare these predicted properties with direct computation of trajectories.

New developments in classical chaotic scattering

Classical chaotic scattering is a topic of fundamental interest in nonlinear physics due to the numerous existing applications in fields such as celestial mechanics, atomic and nuclear physics and fluid mechanics, among others. Many new advances in chaotic scattering have been achieved in the last few decades. This work provides a current overview of the field, where our attention has been mainly focused on the most important contributions related to the theoretical framework of chaotic scattering, the fractal dimension, the basins boundaries and new applications, among others. Numerical techniques and algorithms, as well as analytical tools used for its analysis, are also included. We also show some of the experimental setups that have been implemented to study diverse manifestations of chaotic scattering. Furthermore, new theoretical aspects such as the study of this phenomenon in time-dependent systems, different transitions and bifurcations to chaotic scattering and a classification of boundaries in different types according to symbolic dynamics are also shown. Finally, some recent progress on chaotic scattering in higher dimensions is also described.

Chaotic escape from an open vase-shaped cavity. I. Numerical and experimental results

We present part I in a two-part study of an open chaotic cavity shaped as a vase. The vase possesses an unstable periodic orbit in its neck. Trajectories passing through this orbit escape without return. For our analysis, we consider a family of trajectories launched from a point on the vase boundary. We imagine a vertical array of detectors past the unstable periodic orbit and, for each escaping trajectory, record the propagation time and the vertical detector position. We find that the escape time exhibits a complicated recursive structure. This recursive structure is explored in part I of our study. We present an approximation to the Helmholtz equation for waves escaping the vase. By choosing a set of detector points, we interpolate trajectories connecting the source to the different detector points. We use these interpolated classical trajectories to construct the solution to the wave equation at a detector point. Finally, we construct a plot of the detector position versus the escape time and compare this graph to the results of an experiment using classical ultrasound waves. We find that generally the classical trajectories organize the escaping ultrasound waves.

Chaotic escape from an open vase-shaped cavity. II. Topological theory

We present part II of a study of chaotic escape from an open two-dimensional vase-shaped cavity. A surface of section reveals that the chaotic dynamics is controlled by a homoclinic tangle, the union of stable and unstable manifolds attached to a hyperbolic fixed point. Furthermore, the surface of section rectifies escape-time graphs into sequences of escape segments; each sequence is called an epistrophe. Some of the escape segments (and therefore some of the epistrophes) are forced by the topology of the dynamics of the homoclinic tangle. These topologically forced structures can be predicted using the method called homotopic lobe dynamics (HLD). HLD takes a finite length of the unstable manifold and a judiciously altered topology and returns a set of symbolic dynamical equations that encode the folding and stretching of the unstable manifold. We present three applications of this method to three different lengths of the unstable manifold. Using each set of dynamical equations, we compute minimal sets of escape segments associated with the unstable manifold, and minimal sets associated with a burst of trajectories emanating from a point on the vase's boundary. The topological theory predicts most of the early escape segments that are found in numerical computations.

Escape of quantum particles from an open cavity

A negative ion irradiated by a laser provides a coherent source of electrons propagating out from the location of the negative ion. The total escape rates of the electrons when the negative ion is placed inside an open cavity in the shape of a wedge are studied. It is shown that the wedge induces significant oscillations in the total escape rates because of quantum interference effects. In particular, it is shown that, for a wedge with an opening angle of π/N, where N is an arbitrary positive integer, there are (2N-1) induced oscillations in the rates. As a demonstration, the case for a wedge with an opening angle π/5 is calculated and analyzed in detail.

Intrinsic stickiness and chaos in open integrable billiards: tiny border effects

Rounding border effects at the escape point of open integrable billiards are analyzed via the escape-time statistics and emission angles. The model is the rectangular billiard and the shape of the escape point is assumed to have a semicircular form. Stickiness, chaos, and self-similar structures for the escape times and emission angles are generated inside "backgammon" like stripes of initial conditions. These stripes are born at the boundary between two different emission angles but with the same escape times and when rounding effects increase they start to overlap generating a very rich dynamics. Tiny rounded borders (around 0.1% from the whole billiard size) are shown to be sufficient to generate the sticky motion with power-law decay γ(esc)=1.27, while borders larger than 10% are enough to produce escape times related to the chaotic motion. Escape exponents in the interval 1<γ(esc)<2 are generated due to marginal unstable periodic orbits trapping alternately (in time) regular and chaotic trajectories.

Nonperiodic echoes from quantum mushroom-billiard hats

Nonperiodic tunable quantum echoes have been observed in experiments with an open microwave billiard whose geometry under certain conditions provides Fibonacci-like sequences of classical delay times. These sequences combined with the reflection at the opening induced by the wave character of the experiment and the size of the opening allow to shape quantum pulses. The pulses are obtained by response of an integrable scattering system.