Three-boson problem near a narrow Feshbach resonance

We consider a three-boson system with resonant binary interactions and show that for sufficiently narrow resonances three-body observables depend only on the resonance width and the scattering length. The effect of narrow resonances is qualitatively different from that of wide resonances revealing novel physics of three-body collisions. We calculate the rate of three-body recombination to a weakly bound level and the atom-dimer scattering length and discuss implications for experiments on Bose-Einstein condensates and atom-molecule mixtures near Feshbach resonances.     

Effect of radiation on dust particles in orbital resonances

The effect of electromagnetic radiation on the dynamics of arbitrarily shaped cosmic dust particles is investigated. The paper concentrates on the motion of dust grains near commensurability resonances with a planet—mean-motion resonances—and possible capture of the grains in the resonances. A particle is in resonance with a planet when the ratio of the mean motions of the two objects is a ratio of two small integers.

The most fundamental properties of the orbital evolution of spherical dust particles in the mean-motion resonances are shortly rederived: the solar wind effect is also included and the existing result is improved. The results for spherical particles are compared with the detailed numerical calculations for nonspherical particles. It is shown that the fundamental results valid for spherical grains do not hold, in general, for nonspherical particles. While spherical particles are always characterized by the secular decrease of the semi-major axes near mean-motion resonances, this may not be true for nonspherical particles. Nonspherical grains may exhibit an increase of the semi-major axes before capturing in the mean-motion resonances. This is caused by the effect of electromagnetic radiation on nonspherical dust grains. The eccentricities of spherical particles in the exterior resonances approach a limiting value, but nonspherical grains may not follow this behaviour. The interior resonances are characterized by a systematic decrease of eccentricity for spheres, but various behaviours exist in the case of irregularly shaped particles.

The motion of a nonspherical dust particle under the action of electromagnetic radiation may be characterized by a small change of the semi-major axis during a long-time interval, but the particle is not captured in any mean-motion resonance. This kind of motion does not exist for spherical grains.     

Accumulation of three-body resonances above two-body thresholds

We calculate resonances in the three-body system with attractive Coulomb potential by solving homogeneous Faddeev-Merkuriev integral equations for complex energies. The equations are solved using the Coulomb-Sturmian separable expansion method. This approach allows us to study the exact behavior of the three-body Coulomb systems near the threshold. A negatively charged positronium ion is used as a test case. In addition to locating all previously known S-wave resonances of the positronium ion, we also find a large number of new resonant states that accumulate just slightly above the two-body thresholds. The pattern of accumulation of resonant states above the two-body thresholds suggests that probably they are infinite in number. We conjecture that this may be a general property of the three-body system with an attractive Coulomb potential.     

Borromean three-body heteroatomic resonances

We present an approach to analyze recent experimental evidences of Efimov resonant states in mixtures of ultracold gases, by considering two-species three-body atomic systems bound in a Borromean configuration, where all the two-body interactions are unbound. For such Borromean three-body systems, it is shown that a continuum three-body s-wave resonance emerges from an Efimov state as a scattering length or a three-body scale is moved. The energy and width of the resonant state are determined from a scaling function with arguments given by dimension-less energy ratios relating the two-body virtual state subsystem energies with the shallowest three-body bound state. The peculiar behavior of such resonances is that their peaks are expected to move to lower values of the scattering length, with increasing width, as one raises the temperature. For Borromean systems, two resonant peaks are expected in ultralow-temperature regimes, which will disappear at higher energies. It is shown how a Borromean-Efimov excited bound state turns out to a resonant state by tuning the virtual two-body subsystem energies or scattering lengths, with all energies written in units of the next deeper shallowest Efimov state energy. The resonance position and width for the decay into the continuum are obtained as universal scaling functions (limit cycle) of the dimensionless ratios of the two and three-body scales, which are calculated numerically within a zero-range renormalized three-body model.     

On the accuracy of the IWM–CFC approximation in differentially rotating relativistic stars

A circular restricted three-body problem describes the motion of a test particle around two massive bodies in circular orbits. In this system, orbital decay caused by a gravitational radiation reaction between the two primary bodies is considered but the direct effect of gravitational radiation on the test particle is neglected. We adopt distance- and time-scale transformations to Newtonian problems so that systems without orbital decay will not depend on separation between the primaries but systems with orbital decay will depend on this separation. If a regular or chaotic orbit is given in a Newtonian system, the starting separation of the primaries varies according to the corresponding decay system. Thus, insights into the chaotic behaviour of a third body in a decay case are provided. For a large initial separation between the primaries, the chaos that exists in a Newtonian problem may be retained for a long enough time scale of dissipative evolution before the primaries coalesce. The final state of a third body is escape attributed to orbital decay.     

Efimov effect in nuclear three-body resonance decays

We investigate the effects of the nearly fulfilled Efimov conditions on the properties of three-body resonances. Using the hyper-spheric adiabatic expansion method we compute energy distributions of fragments in a three-body decay of a nuclear resonance. As a realistic example we investigate the 1- state in the halo nucleus 11Li within a three-body model 9Li + n +n model. Characteristic features appear as sharp peaks in the energy distributions. Their origin, as in the Efimov effect, is in the large two-body s-wave scattering lengths between the pairs of fragments.     

Noise-induced enhancement of chemical reactions in nonlinear flows

Motivated by the problem of ozone production in atmospheres of urban areas, we consider chemical reactions of the general type: A+B-->2C, in idealized two-dimensional nonlinear flows that can generate Lagrangian chaos. Our aims differ from those in the existing work in that we address the role of transient chaos versus sustained chaos and, more importantly, we investigate the influence of noise. We find that noise can significantly enhance the chemical reaction in a resonancelike manner where the product of the reaction becomes maximum at some optimal noise level. We also argue that chaos may not be a necessary condition for the observed resonances. A physical theory is formulated to understand the resonant behavior. (c) 2002 American Institute of Physics.     

Special features of galactic dynamics: Disc dynamics

This is a tutorial presentation of special features of galactic disc dynamics, which completes our introduction to galactic dynamics initially presented in [30]. The emphasis is on topics where galactic dynamics and celestial mechanics share common starting points and/or methods of approach. We start by giving some definitions and general notions on the link between observations and dynamical modeling of discs. Then we focus on the application of resonant Hamiltonian perturbation theory in disc resonances. By examining in detail the case of the Inner Lindblad resonance, we demonstrate how resonant perturbation theory leads to an orbital theory of spiral structure in normal galaxies. Passing to barred galaxies, the phase space structure and the role of chaos in the corotation region are analyzed. This is accomplished by a summary of the modern theory of invariant manifolds of unstable periodic orbits in the vicinity of L₁ or L₂, which can interpret the generation of spiral patterns by chaotic orbits beyond corotation. Some additional topics, potentially important for disc dynamics, are briefly commented.     

Resonant capture of multiple planet systems under dissipation and stable orbital configurations

Migration of planetary systems caused by the action of dissipative forces may lead the planets to be trapped in a resonance. In this work we study the conditions and the dynamics of such resonant trapping. Particularly, we are interested in finding out whether resonant capture ends up in a long-term stable planetary configuration. For two planet systems we associate the evolution of migration with the existence of families of periodic orbits in the phase space of the three-body problem. The family of circular periodic orbits exhibits a gap at the 2:1 resonance and an instability and bifurcation at the 3:1 resonance. These properties explain the high probability of 2:1 and 3:1 resonant capture at low eccentricities. Furthermore, we study the resonant capture of three-planet systems. We show that such a resonant capture is possible and can occur under particular conditions. Then, from the migration path of the system, stable three-planet configurations, either symmetric or asymmetric, can be determined.     

Investigation of Light Pressure Influence on Dynamics of Near-Earth Objects with Reverse Motion

Russian Physics Journal - In this paper we consider the joint influence of secular resonances and light pressure on the long-term orbital evolution of objects with reverse motion in the near-Earth...     

Regular and chaotic orbits in the dynamics of exoplanets

Many of exoplanetary systems consist of more than one planet and the study of planetary orbits with respect to their long-term stability is very interesting. Furthermore, many exoplanets seem to be locked in a mean-motion resonance (MMR), which offers a phase protection mechanism, so that, even highly eccentric planets can avoid close encounters. However, the present estimation of their initial conditions, which may change significantly after obtaining additional observational data in the future, locate most of the systems in chaotic regions and consequently, they are destabilized. Hence, dynamical analysis is imperative for the derivation of proper planetary orbital elements. We utilize the model of spatial general three body problem, in order to simulate such resonant systems through the computation of families periodic orbits. In this way, we can figure out regions in phase space, where the planets in resonances should be ideally hosted in favour of long-term stability and therefore, survival. In this review, we summarize our methodology and showcase the fact that stable resonant planetary systems evolve being exactly centered at stable periodic orbits. We apply this process to co-orbital motion and systems HD 82943, HD 73526, HD 128311, HD 60532, HD 45364 and HD 108874.     

Few-body Decay and Recombination in Nuclear Astrophysics

Three-body continuum problems are investigated for light nuclei of astrophysical relevance. We focus on three-body decays of resonances or recombination via resonances or the continuum background. The concepts of widths, decay mechanisms and dynamic evolution are discussed. We also discuss results for the triple ?? decay in connection with 2⁺ resonances and density and temperature dependence rates of recombination into light nuclei from ??-particles and neutrons.     

Efimov Resonances in Ultracold Quantum Gases

Ultracold atomic gases have developed into prime systems for experimental studies of Efimov three-body physics and related few-body phenomena, which occur in the universal regime of resonant interactions. In the last few years, many important breakthroughs have been achieved, confirming basic predictions of universal few-body theory and deepening our understanding of such systems. We review the basic ideas along with the fast experimental developments of the field, focussing on ultracold cesium gases as a well-investigated model system. Triatomic Efimov resonances, atom-dimer Efimov resonances, and related four-body resonances are discussed as central observables. We also present some new observations of such resonances, supporting and complementing the set of available data.     

Cross-molecular coupling in combined photoassociation and Feshbach resonances

We model combined photoassociation and Feshbach resonances in a Bose-Einstein condensate. When the magnetic field is far-off resonance, cross coupling between the two target molecules--enabled by the shared dissociation continuum--leads to an anomalous dispersive shift in the position of laser resonance, as well as unprecedented elimination and enhancement of resonant photoassociation via quantum interference. For off-resonant lasers, a dispersive shift and quantum interference appear similarly in resonant three-body Feshbach losses, except that the Feshbach node is tunable with intensity.     

Chaos in classical cosmology

We study the dynamics of a Friedmann-Robertson-Walker universe conformally coupled to a real, self-interacting, massive scalar field. We apply a full set of tools corresponding to dynamical system theory: fixed points, linear stability analysis, resonances study and numerical evaluation of Poincaré sections of the dynamical flux. We can conclude that the chaotic behaviour is possible in the very early universe. In the case of a spatially closed universe we show that the route to chaos is reached by successive breaking of the resonant tori due to the action of 11 resonances.     

Universality of the three-body parameter for Efimov states in ultracold cesium

We report on the observation of triatomic Efimov resonances in an ultracold gas of cesium atoms. Exploiting the wide tunability of interactions resulting from three broad Feshbach resonances in the same spin channel, we measure magnetic-field dependent three-body recombination loss. The positions of the loss resonances yield corresponding values for the three-body parameter, which in universal few-body physics is required to describe three-body phenomena and, in particular, to fix the spectrum of Efimov states. Our observations show a robust universal behavior with a three-body parameter that stays essentially constant.     

Control of light scattering by nanoparticles with optically-induced magnetic responses

Conventional approaches to control and shape the scattering pattems of light generated by different nanostructures are mostly based on engineering of their electric response due to the fact that most metallic nanostructures support only electric resonances in the optical frequency range. Recently, fuelled by the fast development in the fields of metamaterials and plasmonics, artificial optically-induced magnetic responses have been demonstrated for various nanostructures. This kind of response can be employed to provide an extra degree of freedom for the efficient control and shaping of the scattering patterns of nanoparticles and nanoantennas. Here we review the recent progress in this research direction of nanoparticle scattering shaping and control through the interference of both electric and optically-induced magnetic responses. We discuss the magnetic resonances supported by various structures in different spectral regimes, and then summarize the original results on the scattering shaping involving both electric and magnetic responses, based on the interference of both spectrally separated （with different resonant wavelengths） and overlapped dipoles （with the same resonant wavelength）, and also other higher-order modes. Finally, we discuss the scattering control utilizing Fano resonances associated with the magnetic responses.     

Observation of heteronuclear Feshbach molecules from a 85Rb-87Rb gas

We report on the observation of ultracold heteronuclear Feshbach molecules. Starting with a 87Rb Bose-Einstein condensate and a cold atomic gas of 85Rb, we utilize previously unobserved interspecies Feshbach resonances to create up to 25,000 molecules. Even though the 85Rb gas is nondegenerate, we observe a large molecular conversion efficiency due to the presence of a quantum degenerate 87Rb gas; this represents a key feature of our system. We compare the molecule creation at two different Feshbach resonances with different magnetic-field widths. The two Feshbach resonances are located at 265.44+/-0.15 G and 372.4+/-1.3 G. We also directly measure the small binding energy of the molecules through resonant magnetic-field association.     

The effect of Lagrangian chaos on locking bifurcations in shear flows

The effect of an externally imposed perturbation on an unstable or weakly stable shear flow is investigated, with a focus on the role of Lagrangian chaos in the bifurcations that occur. The external perturbation is at rest in the laboratory frame and can form a chain of resonances or cat's eyes where the initial velocity v(x0)(y) vanishes. If in addition the shear profile is unstable or weakly stable to a Kelvin-Helmholtz instability, for a certain amplitude of the external perturbation there can be an unlocking bifurcation to a nonlinear wave resonant around a different value of y, with nonzero phase velocity. The interaction of the propagating nonlinear wave with the external perturbation leads to Lagrangian chaos. We discuss results based on numerical simulations for different amplitudes of the external perturbation. The response to the external perturbation is strong, apparently because of non-normality of the linear operator, and the unlocking bifurcation is hysteretic. The results indicate that the observed Lagrangian chaos is responsible for a second bifurcation occurring at larger external perturbation, locking the wave to the wall. This bifurcation is nonhysteretic. The mechanism by which the chaos leads to locking in this second bifurcation is by means of chaotic advective transport of momentum from one chain of resonances to the other (Reynolds stress) and momentum transport to the vicinity of the wall via chaotic scattering. These results suggest that locking of waves in rotating tank experiments in the presence of two unstable modes is due to a similar process. (c) 2002 American Institute of Physics.